401-3642-00L  Brownian Motion and Stochastic Calculus

Semester Spring Semester 2013
Lecturers A.‑S. Sznitman
Periodicity yearly course
Language of instruction English


Abstract Stochastic 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.
Objective Brownian motion: construction and properties, stochastic integration, Ito's formula and applications, stochastic differential equations and their links to partial differential equations.
Content Stochastic 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.
Literature DURRETT, 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 / Notice This 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.