Stochastic Processes (MAGIC089)
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This course is part of the MAGIC core.
The course will introduce the basic concept of stochastic processes. As special and important example the Brownian motion is considered. Different constructions for Brownian motion are given and the main properties of Brownian motion are derived and proven. The stochastic integral is introduced and the Ito formula derived.
Spring 2018 (Monday, January 22 to Friday, March 16; Monday, April 23 to Friday, May 4)
Measure theory and integration. Basics of measure theoretical probability.
• Construction of Brownian motion • Path properties • Transformation invariances of Brownian Motion • Path properties of Brownian motion • Tail events and zero-one laws • Stochastic Integration • Ito calculus • Asymptotic properties of processes: the law of iterated logarithm
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