BIMSA > Tadahisa Funaki
Professor Tadahisa Funaki

Group: Statistics, Probability and Data Science

Office: A3-3-303

Email: funaki@bimsa.cn

Research Field: Probability Theory, Mathematical Physics

CV

Biography

Funaki Tadahisa was a professor at University of Tokyo (1995-2017) and at Waseda University (2017-2022) in Japan. His research subject is probability theory mostly related to statistical physics, specifically interacting systems and stochastic PDEs. He was a president of Mathematical Society of Japan (2013-2015), and was an invited sectional lecturer at ICM 2022.

Research Interest

  • Probability Theory, Mathematical Physics

Education Experience

  • 1982 -      Nagoya University      Mathematics      Doctor
  • 1974 - 1976      University of Tokyo      Mathematics      Master
  • 1970 - 1974      University of Tokyo      Mathematics      Bachelor

Work Experience

  • 2022 -      BIMSA      Professor
  • 2017 -      University of Tokyo      Professor Emeritus
  • 2017 - 2022      Waseda University      Professor
  • 1995 - 2017      University of Tokyo      Professor
  • 1992 - 1995      Nagoya University      Professor
  • 1985 - 1992      Nagoya University      Associate Professor
  • 1984 - 1985      Nagoya University      Lecturer
  • 1979 - 1984      Nagoya University      Research Associate
  • 1977 - 1979      Hiroshima University      Research Associate

Honors and Awards

  • 2022      ICM2022 Invited Sectional Lecturer
  • 2007      MSJ (Mathematical Society of Japan) Autumn Prize
  • 2003      Saint-Flour Probability School Lecturer
  • 2002      MSJ (Mathematical Society of Japan) Analysis Prize

Publication

  • [1] Tadahisa Funaki and Sunder Sethuraman, Schauder estimate for quasilinear discrete PDEs of parabolic type, accepted by Memoirs of the American Mathematical Society(2024)
  • [2] T Funaki, Interface motion from Glauber-Kawasaki dynamics of non-gradient type, arXiv:2404.18364 (2024)
  • [3] T Funaki, Hyunjoon Park, Motion of sharp interface of Allen-Cahn equation with anisotropic nonlinear diffusion, arXiv:2403.01732 (2024)
  • [4] T Funaki, Chenlin Gu, Han Wang, Quantitative homogenization and hydrodynamic limit of non-gradient exclusion process, arXiv:2404.12234 (2024)
  • [5] T Funaki, Stochastic PDE approach to fluctuating interfaces, arXiv:2412.00708 (2024)
  • [6] T Funaki, C Landim, S Sethuraman, Linear fluctuation of interfaces in Glauber-Kawasaki dynamics, arXiv:2412.04015 (2024)
  • [7] Tadahisa Funaki, Hydrodynamic limit and stochastic PDEs related to interface motion, ICM---International Congress of Mathematicians 2022, EMS Press, VI(2023), 4302-4325
  • [8] Tadahisa Funaki, Patrick van Meurs, Sunder Sethuraman and Kenkichi Tsunoda, Constant-speed interface flow from unbalanced Glauber-Kawasaki dynamics, Ensaios Matematicos, 38(2023), 223-248
  • [9] Funaki T, van Meurs P, Sethuraman S, et al. , Motion by mean curvature from Glauber-Kawasaki dynamics with speed change, Journal of Statistical Physics, 190(3), 45 (2023)
  • [10] Perla El Kettani, Tadahisa Funaki, Danielle Hilhorst, Hyunjoon Park, Sunder Sethuraman, Mean curvature interface limit from Glauber+Zero-range interacting particles, Communications in Mathematical Physics, 394(1173--1223) (2022)
  • [11] Tadahisa Funaki, Bin Xie, Global solvability and convergence to stationary solutions in singular quasilinear stochastic PDEs., Stochastic partial differential equations: analysis and computations, 10(4), 858--897 (2022)
  • [12] Perla El Kettani, Tadahisa Funaki, Danielle Hilhorst, Hyunjoon Park, Sunder Sethuraman, Singular limit of an Allen-Cahn equation with nonlinear diffusion, Tunisian Journal of Mathematics, 719--754 (2022)
  • [13] Tadahisa Funaki. Large deviation for dynamic model of three dimensional Young diagrams. Advanced Studies in Pure Mathathematics. 2021, 87. Stochastic Analysis, Random Fields and Integrable Probability --- Fukuoka 2019, 227--238, Mathematical Society of Japan.
  • [14] Cedric Bernardin, Tadahisa Funaki, Sunder Sethuraman, Derivation of coupled KPZ-Burgers equation from multi-species zero-range processes, Annals of Applied Probability, 31, 1966--2017 (2021)
  • [15] Tadahisa Funaki, Yuto Nishijima, Hayate Suda, Stochastic eight-vertex model, its invariant measures and KPZ limit., Journal of Statistical Physics, 184(11), 1--30 (2021)
  • [16] Tadahisa Funaki, Masato Hoshino, Sunder Sethuraman and Bin Xie. Asymptotics of PDE in random environment by paracontrolled calculus. Annales de l'Institut Henri Poincare - Probabilites et Statistiques. 2021, 57, 1702--1735.
  • [17] T Funaki, Y Gao, D Hilhorst, Existence and uniqueness of the entropy solution of a stochastic conservation law with a Q-Brownian motion, Math Meth Appl Sci, 43, 5860--5886 (2020)
  • [18] T Funaki, S Yokoyama, Sharp interface limit for stochastically perturbed mass conserving Allen-Cahn equation, Ann Probab, 47, 560--612 (2019)
  • [19] T Funaki, Profile of Prof Hirofumi Osadas achievements---Stochastic analysis of infinite particle systems with long range interaction. (Japanese), Sugaku, 71, 202--209 (2019)
  • [20] T Funaki, Invariant measures in coupled KPZ equations, Stochastic Dynamics Out of Equilibrium, Springer, 560--568 (2019)
  • [21] T Funaki, K Tsunoda, Motion by mean curvature from Glauber-Kawasaki dynamics, J Statis Phys, 177, 183--208 (2019)
  • [22] A De Masi, T Funaki, E Presutti, ME Vares, Fast-reaction limit for Glauber-Kawasaki dynamics with two components, ALEA Lat Am J Probab Math Stat, 16, 957--976 (2019)
  • [23] T Funaki, Y Otobe, B Xie, Stochastic Partial Differential Equations, in Japanese, Iwanami, xiv+335 pages (2019)
  • [24] C Denis, T Funaki, S Yokoyama, Curvature motion perturbed by a direction-dependent colored noise, Stochastic Partial Differential Equations and Related Fields, Springer Proceedings in Mathematics & Statistics, 229, 177--200 (2018)
  • [25] T Funaki, Y Gao, D Hilhorst, Convergence of a finite volume scheme for a stochastic conservation law involving a Q-Brownian motion, Discrete Contin Dyn Syst Ser B, 23, 1459--1502 (2018)
  • [26] T Funaki, Hydrodynamic limit for exclusion processes, Communications in Mathematics and Statistics, 6, 417--480 (2018)
  • [27] T Funaki, M Hoshino, A coupled KPZ equation, its two types of approximations and existence of global solutions, J Funct Anal, 273, 1165--1204 (2017)
  • [28] JY Wakano, T Funaki, S Yokoyama, Derivation of replicator-mutator equations from a model in population genetics, Japan J Ind Appl Math, 34, 473--488 (2017)
  • [29] T Funaki, Lectures on Random Interfaces, SpringerBriefs in Probability and Mathematical Statistics, xii+138 pages (2016)
  • [30] T Funaki, M Ohnawa, Y Suzuki, S Yokoyama, Existence and uniqueness of solutions to stochastic Rayleigh-Plesset equations, J. Math. Anal. Appl., 425, 20--32 (2015)
  • [31] E Bolthausen, T Chiyonobu, T Funaki, Scaling limits for weakly pinned Gaussian random fields under the presence of two possible candidates, J. Math. Soc. Japan, 67, 1359--1412 (2015)
  • [32] T Funaki, J Quastel, KPZ equation, its renormalization and invariant measures, Stoch PDE Anal Comp, 3, 159--220 (2015)
  • [33] T Funaki, Infinitesimal invariance for the coupled KPZ equations, Memoriam Marc Yor -- Seminaire de Probabilites XLVII, Lect Notes Math, 2137, 37--47 (2015)
  • [34] T Funaki, Equivalence of ensembles under inhomogeneous conditioning and its applications to random Young diagrams, J. Stat. Phys., 154, 588--609 (2014)
  • [35] P El Kettani, T Funaki, D Hilhorst, H Park, S Sethuraman, Singular limit of an Allen–Cahn equation with nonlinear diffusion, Tunisian Journal of Mathematics, 4(4), 719-754 (2023)
  • [36] T FUNAKI, In a similar context, existence and uniqueness theorems have been obtained for the martingale problem associating diffusion processes with a type of nonlinear parabolic … (2023)
  • [37] P El Kettani, T Funaki, D Hilhorst, H Park, S Sethuraman, Mean curvature interface limit from Glauber+ Zero-range interacting particles, Communications in Mathematical Physics, 394(3), 1173-1223 (2022)
  • [38] T Funaki, B Xie, Global solvability and convergence to stationary solutions in singular quasilinear stochastic PDEs, Stochastics and Partial Differential Equations: Analysis and Computations, 10 (2022)
  • [39] T Funaki, M Hoshino, S Sethuraman, B Xie, Asymptotics of PDE in random environment by paracontrolled calculus, Annales de l'Institut Henri Poincare (B) Probabilites et statistiques, 57(3) (2021)
  • [40] T Funaki, Y Nishijima, H Suda, Stochastic eight-vertex model, its invariant measures and KPZ limit, Journal of Statistical Physics, 184, 1-30 (2021)
  • [41] T Funaki, Large deviation for dynamic model of three dimensional Young diagrams, Stochastic Analysis, Random Fields and Integrable Probability—Fukuoka 2019 (2021)
  • [42] T Funaki, Y Gao, D Hilhorst, Existence and uniqueness of the entropy solution of a stochastic conservation law with a$Q$‐Brownian motion, Mathematical Methods in the Applied Sciences, 43(9), 5860-5886 (2020)
  • [43] T Funaki, K Tsunoda, Motion by mean curvature from Glauber–Kawasaki dynamics, Journal of Statistical Physics, 177, 183-208 (2019)
  • [44] T Funaki, S Yokoyama, Sharp interface limit for stochastically perturbed mass conserving Allen–Cahn equation, Annals of Probability, 47(1), 560-612 (2019)
  • [45] T Funaki, S Yokoyama, Supplement to “Sharp interface limit for stochastically perturbed mass conserving Allen–Cahn equation.”, DOI (2019)
  • [46] JY Wakano, T Funaki, S Yokoyama, Derivation of replicator–mutator equations from a model in population genetics, Japan Journal of Industrial and Applied Mathematics, 34, 473-488 (2017)
  • [47] T Funaki, T Funaki, Sharp interface limits for a stochastic Allen-Cahn equation, Lectures on Random Interfaces, 93-110 (2016)
  • [48] T Funaki, T Funaki, Stochastic Partial Differential Equations, Lectures on Random Interfaces, 81-92 (2016)
  • [49] T Funaki, T Funaki, Scaling Limits for Pinned Gaussian Random Interfaces in the Presence of Two Possible Candidates, Lectures on Random Interfaces, 1-28 (2016)
  • [50] T Funaki, T Funaki, KPZ Equation, Lectures on Random Interfaces, 111-124 (2016)
  • [51] T Funaki, T Funaki, Dynamic Young Diagrams, Lectures on Random Interfaces, 29-79 (2016)
  • [52] T Funaki, M Ohnawa, Y Suzuki, S Yokoyama, Existence and uniqueness of solutions to stochastic Rayleigh–Plesset equations, Journal of Mathematical Analysis and Applications, 425(1), 20-32 (2015)
  • [53] T Funaki, Special Issue on the Centennial Anniversary of the Birth of Kiyosi Ito Foreword, JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 67(4) (2015)
  • [54] T Funaki, Topics in random interfaces (2015)
  • [55] T Funaki, Stationary measures of the KPZ equation (Nonlinear Partial Differential Equations, Dynamical Systems and Their Applications), 数理解析研究所講究録, 1881, 115-120 (2014)
  • [56] T Funaki, M Sasada, M Sauer, B Xie, Fluctuations in an evolutional model of two-dimensional Young diagrams, Stochastic Processes and their Applications, 123(4), 1229-1275 (2013)
  • [57] T Funaki, H Izuhara, M Mimura, C Urabe, A link between microscopic and macroscopic models of self-organized aggregation, Networks and Heterogeneous Media, 7(4), 705-740 (2012)
  • [58] T Funaki, W Woyczynski, Nonlinear Stochastic PDEs: Hydrodynamic Limit and Burgers’ Turbulence, Springer Science & Business Media (2012)
  • [59] T Funaki, Hydrodynamic Limit for the∇ φ Interface Model via Two-Scale Approach, Probability in Complex Physical Systems: In Honour of Erwin Bolthausen and … (2012)
  • [60] T Funaki, Some topics in stochastic partial differential equations, Waseda University (2012)
  • [61] T Funaki, M Sasada, Hydrodynamic limit for an evolutional model of two-dimensional Young diagrams, Communications in Mathematical Physics, 299(2), 335-363 (2010)
  • [62] T Funaki, T Otobe, Scaling limits for weakly pinned random walks with two large deviation minimizers, Journal of the Mathematical Society of Japan, 62(3), 1005-1041 (2010)
  • [63] T Funaki, Introduction to the Theory of Stochastic Differential Equations and Stochastic Partial Differential Equations (2010)
  • [64] T Funaki, Y Giga, MH Giga, H Ishii, RV Kohn, P Rybka, T Sakajo et al., Proceedings of minisemester on evolution of interfaces, Sapporo 2010, Hokkaido University Technical Report Series in Mathematics (2010)
  • [65] E Bolthausen, T Funaki, T Otobe, Concentration under scaling limits for weakly pinned Gaussian random walks, Probability theory and related fields, 143(3), 441-480 (2009)
  • [66] T Funaki, B Xie, A stochastic heat equation with the distributions of Lévy processes as its invariant measures, Stochastic processes and their applications, 119(2), 307-326 (2009)
  • [67] T Funaki, A scaling limit for weakly pinned Gaussian random walks (Proceedings of RIMS Workshop on Stochastic Analysis and Applications), 数理解析研究所講究録別冊, 6, 97-109 (2008)
  • [68] T Funaki, K Ishitani, Integration by parts formulae for Wiener measures on a path space between two curves, Probability Theory and Related Fields, 137, 289-321 (2007)
  • [69] T Funaki, Dichotomy in a scaling limit under Wiener measure with density, NULL (2007)
  • [70] T Funaki, K Toukairin, Dynamic approach to a stochastic domination: the FKG and Brascamp-Lieb inequalities, Proceedings of the American Mathematical Society, 135(6), 1915-1922 (2007)
  • [71] T Funaki, Y Hariya, F Hirsch, M Yor, On some Fourier aspects of the construction of certain Wiener integrals, Stochastic processes and their applications, 117(1), 1-22 (2007)
  • [72] T Funaki, Hydrodynamic limit and nonlinear PDEs with singularities, Asymptotic Analysis and Singularities—Elliptic and parabolic PDEs and … (2007)
  • [73] T Funaki, Construction of stochastic processes associated with the Boltzmann equation and its applications, Stochastic Processes and Their Applications: Proceedings of the (2006)
  • [74] T Funaki, On diffusive motion of closed curves, Proceedings of the Fifth (2006)
  • [75] T Funaki, Y Hariya, M Yor, Wiener integrals for centered Bessel and related processes, II, ALEA Lat. Am. J. Probab. Math. Stat, 1, 225-240 (2006)
  • [76] T Funaki, M Kikuchi, J Potthoff, Direction-dependent modulus of continuity for random fields, Preprint (2006)
  • [77] T Funaki, Y Hariya, F Hirsch, M Yor, On the construction of Wiener integrals with respect to certain pseudo-Bessel processes, Stochastic processes and their applications, 116(12), 1690-1711 (2006)
  • [78] T Funaki, The hydrodynamical limit for scalar ginzburg-landau model on R, Proceedings of the Japanese-French Seminar (2006)
  • [79] T Funaki, Stochastic interface models, Lectures on probability theory and statistics, 103-274 (2005)
  • [80] A Dembo, T Funaki, Favorite points, cover times and fractals, Lectures on Probability Theory and Statistics: Ecole d'Eté de Probabilités … (2005)
  • [81] T Funaki, Y Hariya, M Yor, Wiener integrals for centered powers of Bessel processes, I, Kyushu University (2005)
  • [82] A Dembo, T Funaki, Lectures on Probability Theory and Statistics: Ecole D'Eté de Probabilités de Saint-Flour XXXIII-2003, Springer Science & Business Media (2005)
  • [83] T Funaki, On the stochastic partial differential equations of Ginzburg-Landau type, Stochastic Partial Differential Equations and Their Applications … (2005)
  • [84] T Funaki, Concentration property for Wiener measure with density having two large deviation minimizers, preprint, available on the webpage of the author (2005)
  • [85] T Funaki, H Sakagawa, Large Deviations for$\nabla_{\varphi}$Interface Model and Derivation of Free Boundary Problems, Stochastic analysis on large scale interacting systems, 39, 173-212 (2004)
  • [86] T Funaki, Zero temperature limit for interacting Brownian particles. I. Motion of a single body, NULL (2004)
  • [87] T Funaki, Zero temperature limit for interacting Brownian particles. II. Coagulation in one dimension, NULL (2004)
  • [88] T Funaki, H Osada, Stochastic analysis on large scale interacting systems, Mathematical Society of Japan (2004)
  • [89] T Funaki, H Osada, Volume 39 title pages, Stochastic Analysis on Large Scale Interacting Systems, 39 (2004)
  • [90] T Funaki, Hydrodynamic limit for∇ φ interface model on a wall, Probability theory and related fields, 126(2), 155-183 (2003)
  • [91] T Funaki, Stochastic models for phase separation and evolution equations of interfaces, Sugaku Expositions, 16(1) (2003)
  • [92] T Funaki, Derivation of variational problems from microscopic interface model (Viscosity Solutions of Differential Equations and Related Topics), 数理解析研究所講究録, 1323, 76-83 (2003)
  • [93] T Funaki, S Olla, Fluctuations for∇ φ interface model on a wall, Stochastic processes and their applications, 94(1), 1-27 (2001)
  • [94] T Funaki, T Nishikawa, Large deviations for the Ginzburg–Landau∇ φ interface model, Probability theory and related fields, 120, 535-568 (2001)
  • [95] T Funaki, Recent results on the Ginzburg-Landau▽ φinterface model, Hydrodynamic limits and related topics (2000)
  • [96] T Funaki, Singular limit for stochastic reaction-diffusion equation and generation of random interfaces, Acta Mathematica Sinica, 15, 407-438 (1999)
  • [97] P Biler, T Funaki, WA Woyczynski, Interacting particle approximation for nonlocal quadratic evolution problems, Probability and Mathematical Statistics-Wroclaw University, 19(2), 267-286 (1999)
  • [98] T Funaki, Free boundary problem from stochastic lattice gas model, Annales de l'Institut Henri Poincare, 35(5) (1999)
  • [99] P Biler, T Funaki, WA Woyczynski, Fractal burgers equations, Journal of differential equations, 148(1), 9-46 (1998)
  • [100] T Funaki, WA Woyczyński, Interacting particle approximation for fractal Burgers equation, Stochastic Processes and Related Topics: In Memory of Stamatis Cambanis (1998)
  • [101] P Biler, SV Bolotin, JW Bruce, T Canarius, S Carl, K Chen, K Chen et al., article no. DE983528, Journal of Differential Equations, 148 (1998)
  • [102] T Funaki, H Spohn, Motion by mean curvature from the Ginzburg-Landau interface model, Communications in Mathematical Physics, 185(1), 1-36 (1997)
  • [103] T Funaki, Singular limit for reaction-diffusion equation with self-similar Gaussian noise, Taniguchi Symposium, New Trends in Stochastic Analysis, 132-152 (1997)
  • [104] T Funaki, Singular limit for stochastic reaction-diffusion equations, Proceedings of the workshop on nonlinear partial differential equations, 34-39 (1997)
  • [105] T FUNAKI, Department of Mathematics, School of Science, New Trends In Stochastic Analysis (1997)
  • [106] T Funaki, K Uchiyama, HT Yau, Hydrodynamic limit for lattice gas reversible under Bernoulli measures, Nonlinear Stochastic PDEs: Hydrodynamic Limit and Burgers’ Turbulence, 1-40 (1996)
  • [107] T Funaki, Equilibrium fluctuations for lattice gas, Itô’s stochastic calculus and probability theory, 63, 63-72 (1996)
  • [108] WA Woyczyński, T Funaki, Nonlinear Stochastic PDE's: Hydrodynamic Limit and Burgers' Turbulence, Springer (1996)
  • [109] T Funaki, The scaling limit for a stochastic PDE and the separation of phases, Probability Theory and Related Fields, 102(2), 221-288 (1995)
  • [110] T Funaki, D Surgailis, WA Woyczynski, Gibbs-Cox random fields and Burgers turbulence, The Annals of Applied Probability, 461-492 (1995)
  • [111] J Fritz, T Funaki, JL Lebowitz, Stationary states of random Hamiltonian systems, Probability Theory and Related Fields, 99(2), 211-236 (1994)
  • [112] T Funaki, Low temperature limit and separation of phases for Ginzburg-Landau stochastic equation, Stochastic analysis on infinite-dimensional spaces (1994)
  • [113] T Funaki, H Nagai, Degenerative convergence of diffusion process toward a submanifold by strong drift, Stochastics: An International Journal of Probability and Stochastic … (1993)
  • [114] T Funaki, A stochastic partial differential equation with values in a manifold, Journal of functional analysis, 109(2), 257-288 (1992)
  • [115] T FUNAKI, where [a]= Σ= 1 αι and Da=()...(2) for multi-indices a=(a1,..., α)€, Stochastic Partial Differential Equations and Their Applications … (1992)
  • [116] T Funaki, Regularity properties for stochastic partial differential equations of parabolic type, Topology, 1011-1023 (1991)
  • [117] T Funaki, The reversible measures of multi-dimensional Ginzburg-Landau type continuum model, Topology, 37(5), 1011-1023 (1991)
  • [118] T Funaki, K Handa, K Uchiyama, Hydrodynamic limit of one-dimensional exclusion processes with speed change, The Annals of Probability, 245-265 (1991)
  • [119] T Funaki, The hydrodynamic limit for a system with interactions prescribed by Ginzburg-Landau type random Hamiltonian, Probability theory and related fields, 90(4), 519-562 (1991)
  • [120] T FUNAKI, K HANDA, K UCHIYAMA, Nagoya University, Nagoya University and Tokyo Institute of Technology, The Annals of Probability, 19(1), 245-265 (1991)
  • [121] T Funaki, Hydrodynamic limit for Ginzburg-Landau type continuum model, Probability theory and mathematical statistics, 1, 382-390 (1990)
  • [122] T Funaki, Derivation of the hydrodynamical equation for one-dimensional Ginzburg-Landau model, Probability theory and related fields, 82(1), 39-93 (1989)
  • [123] T Funaki, The central limit theorem for the spatially homogeneous Boltzmann equation, Probabilistic methods in mathematical physics (1987)
  • [124] T Funaki, The diffusion approximation of the spatially homogeneous Boltzmann equation, Topology, 37(5), 1011-1023 (1985)
  • [125] T FUNAKI, SOME LIMIT-THEOREMS FOR MARKOV-PROCESSES ASSOCIATED WITH THE BOLTZMANN-EQUATION, STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 21(1), 3-4 (1985)
  • [126] T Funaki, A certain class of diffusion processes associated with nonlinear parabolic equations, Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 67(3), 331-348 (1984)
  • [127] T Funaki, Random motion of strings and stochastic differential equations on the space C ([0, 1], Rd), North-Holland Mathematical Library, 32, 121-133 (1984)
  • [128] T FUNAKI, Taniguchi Symp. SA Katata 1982, pp. 121-133, Stochastic Analysis: Proceedings of the Taniguchi International Symposium on … (1984)
  • [129] T Funaki, Random motion of strings and related stochastic evolution equations, Nagoya Mathematical Journal, 89, 129-193 (1983)
  • [130] T Funaki, The diffusion approximation of the Boltzmann equation of Maxwellian molecules, Publications of the Research Institute for Mathematical Sciences, 19(2), 841-886 (1983)
  • [131] T FUNAKI, 16 TADAHISA FUNAKI, E7EEhE1hh EhEEEEEEEEl h, 16 (1983)
  • [132] T Funaki, Probabilistic construction of the solution of some higher order parabolic differential equation, Topology, 37(5), 1011-1023 (1979)
  • [133] A Inoue, T Funaki, On a new derivation of the Navier-Stokes equation, Communications in Mathematical Physics, 65, 83-90 (1979)
  • [134] T Funaki, Construction of a solution of random transport equation with boundary condition, Journal of the Mathematical Society of Japan, 31(4), 719-744 (1979)
  • [135] S Assing, V Barbu, L Beznea, VI Bogachev, Z Brzezniak, YA Butko et al., Stochastic Partial Differential Equations and Related Fields
  • [136] T Funaki, Interacting particle systems and their large scale behavior II—Part III-B—
  • [137] P El Kettani, T Funaki, D Hilhorst, H Park, S Sethuraman, Tunisian Journal of Mathematics
  • [138] T Funaki, H Osada, ADVANCED STUDIES IN PURE MATHEMATICS 39

 

Update Time: 2025-08-03 17:00:06