# Module for [Scientific Computing]

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## [Probability Theory II] - [2015 Sommer]

Module | Code MH13a | Name Probability Theory II | ||

| Credit Points 8 CP | Workload 240 h | Duration 1 semester | Cycle 0 |

Methods | Lecture 4 h + Exercise course 2 h | |||

Objectives | To have a firm understanding of stochastic calculus for continuous processes | |||

Content | â¢ Definition and properties of the Brownian motion; martingale property of the Brownian motion â¢ Markovian properties of the Brownian motion; law of iterated logarithm â¢ Smoothness properties of the Brownian motion â¢ Definition and properties of stochastic integrals; ItÃ´ isometry â¢ ItÃ´ formula and exponential martingales â¢ Stochastic differential equations; existence and uniqueness of weak/strong solutions | |||

Learning outcomes | â¢ A firm understanding of stochastic calculus for continuous processes | |||

Prerequisites | ||||

Suggested previous knowledge | MC4 or equivalent; MD2 or equivalent | |||

Assessments | TBD (typically, homework and written exam) | |||

Literature | I. Karatzas and S. Shreve: Brownian motion and stochastic calculus. Springer, Berlin 1988. D. Revuz and M. Yor: Continuous martingales and Brownian motion. Springer, Berlin 1991. |