from August 22, 2011 to September 3, 2011 (Europe/Ljubljana)
Europe/Ljubljana timezone
Mikhail Urusov: Stochastic differential equations

In the lectures we will mostly consider one-dimensional SDEs. If time permits, the following topics will be discussed:

  • Strong and weak solutions of SDEs;
  • Construction of weak solutions via state space transformation and random time change;
  • Uniqueness and local uniqueness;
  • Convergence of integral functionals;
  • Behavior of solutions;
  • Separating times and measure changes;
  • Martingale property of certain Girsanov-type exponentials;
  • Applications in stochastic finance.

Prerequisites: It is essential to understand fundamental properties of Brownian motion and the Itô integral. Some familiarity with local martingales, continuous semimartingales, and local times is desirable.

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