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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