Ruprecht-Karls-Universität Heidelberg
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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 • Definition and properties of the Brownian motion; martingale property of the Brownian motion • Markovian properties of the Brownian motion; law of iterated logarithm • Smoothness properties of the Brownian motion • Definition and properties of stochastic integrals; Itô isometry • Itô formula and exponential martingales • Stochastic differential equations; existence and uniqueness of weak/strong solutions
Learning outcomes • 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.
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