Brownian Motion and Stochastic Calculus

First lecture:
Tuesday, February 18.
First tutorial:
Friday, February 21.

Course attendence confirmation (Testat) requirements:
No.

Exercises:
Click here for information on the exercises.

Question times ("Präsenz"):
Mondays and Thursdays, 12:00 – 13:00, in HG G 32.6.
Question times during vacation ("Ferienpräsenz"):
see Ferienpräsenz

Course content

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.

Lecture notes

One can buy the Lecture notes during Question times ("Präsenz") for 20 CHF. Additional notes about weak convergence can be found here.

References

• 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, 1981.
• KARATZAS, I.- SHREVE, S.:"Brownian motion and stochastic calculus", Springer, Berlin, 1991.
• REVUZ, D.- YOR, M.:"Continuous Martingales and Brownian Motion", Springer, Berlin, 2005.
• ROGERS, L.C.G.- WILLIAMS, D. :"Diffusions, Markov Processes, and Martingales", vol. 1 and 2, Cambridge University Press, 2000.
  
• 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, 2006.