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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: [1] S. N. Ethier, T. G. Kurtz, Markov Processes: Characterization and Convergence, Hoboken N. J.: Wiley 2005. Additional literature: [2] P. Billingsley, Convergence of Probability Measures, New York: Wiley 1999. [3] O. Kallenberg, Foundations of Modern Probability, New York Berlin Heidelberg: Springer 2002. [4] 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. [5] A. V. Kolesnikov, Weak convergence of diffusion processes on Wiener space. Probab. Th. Rel. Fields 140 No 1-2 (2008), 1-17. [6] 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 [1]): 3 lectures, 1 problem seminar / presentations by participants. Topic 4 - Applications to infinite dimensional stochastic processes (from [4]-[6]): 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.

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Last updated: 2022-11-15