Beijing Institute of Mathematical Sciences and Applications Beijing Institute of Mathematical Sciences and Applications

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About
President
Governance
Partner Institutions
Visit
People
Management
Faculty
Postdocs
Visiting Scholars
Staff
Research
Research Groups
Courses
Seminars
Join Us
Faculty
Postdocs
Students
Events
Conferences
Workshops
Forum
Life @ BIMSA
Accommodation
Transportation
Facilities
Tour
News
News
Announcement
Downloads
Qiuzhen College, Tsinghua University
Yau Mathematical Sciences Center, Tsinghua University (YMSC)
Tsinghua Sanya International  Mathematics Forum (TSIMF)
Shanghai Institute for Mathematics and  Interdisciplinary Sciences (SIMIS)
BIMSA > Probability 3: A course on Brownian Motion and Stochastic Calculus
Probability 3: A course on Brownian Motion and Stochastic Calculus
Gaussian vectors.
Brownian motion: Construction, continuity, nondifferentiability.
Strong Markov property
Multidimensional BM: harmonic functions, recurrence and transience
Skorokhod embedding and the Law of the iterated logarithm

Stochastic integral and Ito formula with respect to BM
Conformal invariance of Brownian motion paths
Continuous time martingales and local martingales
Stochastic integration with respect to local martingales and semimartingales
General Ito formula
Girsanov theorem

Basic properties of Hausdorff dimension
Hausdorff dimension of the zero-set, path and graph of BM
Local time of BM
Intersections of BM paths 
Exceptional sets on BM paths

Grading based on Homework, Class Participation, Midterm and Final Exam
Professor Lars Aake Andersson
Lecturer
Yuval Peres
Date
11th September ~ 25th December, 2024
Location
Weekday Time Venue Online ID Password
Wednesday 09:50 - 12:15 Online ZOOM 08 787 662 9899 BIMSA
Prerequisite
Conditional expectation and Discrete Martingales
Reference
1. J. F. Le Gall: Brownian Motion, Martingales and Stochastic Calculus (Springer)
2. P. Moerters and Y. Peres: Brownian motion (Cambridge University Press.)
Audience
Graduate
Video Public
Yes
Notes Public
Yes
Language
English
Lecturer Intro
Yuval Peres obtained his PhD in 1990 from the Hebrew University, Jerusalem. He was a postdoctoral fellow at Stanford and Yale, and was then a Professor of Mathematics and Statistics in Jerusalem and in Berkeley. Later, he was a Principal researcher at Microsoft. In 2023, he joined Beijing Institute of Mathematical Sciences and Applications. He has published more than 350 papers in most areas of probability theory, including random walks, Brownian motion, percolation, and random graphs. He has co-authored books on Markov chains, probability on graphs, game theory and Brownian motion, which can be found at https://www.yuval-peres-books.com. His presentations are available at https://yuval-peres-presentations.com. He is a recipient of the Rollo Davidson prize and the Loeve prize. He has mentored 21 PhD students including Elchanan Mossel (MIT, AMS fellow), Jian Ding (PKU, ICCM gold medal and Rollo Davidson prize), Balint Virag and Gabor Pete (Rollo Davidson prize). He was an invited speaker at the 2002 International Congress of Mathematicians in Beijing, at the 2008 European congress of Math, and at the 2017 Math Congress of the Americas. In 2016, he was elected to the US National Academy of Science.
Beijing Institute of Mathematical Sciences and Applications
CONTACT

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北京雁栖湖应用数学研究院 101408

Tel. 010-60661855
Email. administration@bimsa.cn

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