Weak convergence of measures and stochastic processes/
Svag konvergens av mått och stokastiska processer
Number of credits: 8 hp
Examiner: Jörg-Uwe Löbus
Course literature: Main literature:  S. N. Ethier, T. G. Kurtz, Markov Processes: Characterization and Convergence, Hoboken N. J.: Wiley 2005. Additional literature:  P. Billingsley, Convergence of Probability Measures, New York: Wiley 1999.  O. Kallenberg, Foundations of Modern Probability, New York Berlin Heidelberg: Springer 2002.  A. Eberle, Diffusions on path and loop spaces: existence, finite dimensional approximation and Holder continuity. Probab. Th. Rel. Fields 109 No. 1 (1997), 77-99.  A. V. Kolesnikov, Weak convergence of diffusion processes on Wiener space. Probab. Th. Rel. Fields 140 No 1-2 (2008), 1-17.  T. S. Zhang, Finite dimensional approximations of diffusion processes on Ba- nach spaces. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 4 No. 4 (2001), 521-531.
Course contents: Topic 1 - Prokhorov's theorem, Weak convergence of measure and probability measures: 3 lectures, 1 problem seminar. Topic 2 - Skorokhod space, Weak convergence of stochastic processes: 3 lectures, 1 problem seminar. Topic 3 - Applications to finite dimensional stochastic processes (from ): 3 lectures, 1 problem seminar / presentations by participants. Topic 4 - Applications to infinite dimensional stochastic processes (from -): 3 lectures, 1 problem seminar / presentations by participants.
Examination: Examination is based on contributions to problem seminars and presentation.
Prerequisites: Measure and integration theory MAI0067 or comparable, Probability theory and Stochastic processes MAI0045 and MAI0090 or comparable, Malliavin calculus (for Topic 4) MAI0104 or comparable.
Last updated: 2022-11-15