401-3642-00L  Brownian Motion and Stochastic Calculus

SemesterSpring Semester 2013
LecturersA.‑S. Sznitman
Periodicityyearly course
Language of instructionEnglish


AbstractStochastic analysis is an important tool in the study of stochastic processes. The lecture will cover some basic objects of stochastic analysis.
The following topics will for instance be discussed:
Brownian motion: construction and properties, stochastic integration, Ito's formula and applications,stochastic differential equations and their links to partial differential equations.
ObjectiveBrownian motion: construction and properties, stochastic integration, Ito's formula and applications, stochastic differential equations and their links to partial differential equations.
ContentStochastic analysis is an important tool in the study of stochastic processes. The lecture will cover some basic objects of stochastic analysis. The following topics will for instance be discussed: Brownian motion: construction and properties, stochastic integration, Ito's formula and applications,stochastic differential equations and their links to partial differential equations.
LiteratureDURRETT, R.:"Brownian motion and martingales in analysis", Wadsworth, Belmont, 1984.
IKEDA, N.- WATANABE, S.: "Stochastic Differential Equations and Diffusion Processes", second edition, North Holland, Amsterdam, 1979.
KARATZAS, I.- SHREVE, S.:"Brownian motion and stochastic calculus", Springer, Berlin, 1988.
REVUZ, D.- YOR, M.:"Continuous Martingales and Brownian Motion", Springer, Berlin, 1991.
ROGERS, L.C.G.- WILLIAMS, D. :"Diffusions, Markov Processes, and Martingales", vol. 1 and 2, Wiley, Chichester, 1987, 1994. STROOCK,D.W.:"Lectures on Stochastic Analysis: Diffusion Theory", London Mathematical Society Student Texts 6, Cambridge University Press, 1987. STROOCK,D.W.- VARADHAN, S.R.S.: "Multidimensional Diffusion Processes", Springer, Berlin, 1979.
Prerequisites / NoticeThis course replaces the former course 401-3642-00L Stochastic Processes and Stochastic Analysis. Moreover it has a large overlap with the course 401-4608-10L Brownian Motion and Stochastic Calculus from FS 2010. Therefore it is forbidden to register for an examination for more than one of the three courses mentioned.