Theoretical and Mathematical Physics

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WP34 Stochastic Integration and Stochastic Differential Equations (ME3)

The module covers the following topics: Doob inequalities, Doob-Meyer decomposition in continuous time, quadratic variation and covariation, Ito isometry and stochastic integral with semimartingales as integrator, Ito formula in the general case, Stratonovich integral, Ito calculus, stochastic treatment of parabolic and elliptic PDEs, Levy's theorem, random time changes in stochastic integrals. Further topics are change of measure: Girsanov's theorem, white noise, stochastic differential equations: existence and uniqueness of strong solutions, weak solutions. The module conveys familiarity with the methods of modern stochastic analysis, especially in the analysis of stochastic phenomena in continuous time.
  • SS
  • 9ECTS