Math 591A: Stochastic Analysis and Its Applications

Zhen-Qing Chen

Autumn 2000, Monday/Wednesday/Friday 9:30-10:20


Stochastic analysis is a core of modern probability theory and its importance is increasingly evident. Stochastic analysis is applied to an increasing family of other scientific areas, for example in finance, biosciences, engineering, etc.  Stochastic analysis also has important interactions with other branches of mathematics, for example, PDE, geometry, complex analysis, and harmonic analysis.

In this course, I plan to cover topics on stochastic integrals, Ito's formula, martingale representation theorem and Girsanov transform, stochastic differential equations, probabilistic methods in PDE, and some applications to mathematical finance.

Textbooks:  I will use the following as reference books for this course.

  1. B. Oksendal, Stochastic Differential Equations, Fifth Edition. Springer-Verlag, Berlin, 1998.

    2.  
  2. Richard Durrett,  Stochastic calculus: A practical introduction.  CRC Press, 1996.

    3.  
  3. I. Karatzas and S. Shreve, Brownian Motion and Stochastic Calculus, Second Edition. Springer-Verlag, New York, 1994.
Prerequisites:  Knowledge about martingales and Brownian motion is required to take this course. Math/Stat 521-2-3 or equivalent is desirable.