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Tutorial Course
2015 NCTS/CMMSC Short Course in Probability

Speaker Professor Yuan-chung Sheu
Affiliation National Chiao Tung University
Date 2015-06-01
Time 13:00-15:30pm

2015-05-18
2015-05-25
2015-06-01
Venue SA212
Abstract Title: Introduction to Stochastic Differential Equations

Topics:
I.Motivation and general definition
II. The Lipschitz case
III. The solutions of SDE as Markov processes
IV. Examples: The Ornstein-Uhlenbeck processes, The geometric Brownian motion and the Bessel processes

The goal of this short course is to give an introduction to the inportant ideas in the theory of stochastic differential equations. After the general definitions, we treat in detail the case of Lipschitz coefficients, under which the existence and uniqueness of strong solutions are obtained. Then we show that the solution of SDE is a Feller process with a second order differential operator as its generator.

References:
1. I.Karatzas and S. Shreve: Brownian motion and stochastic calculus. Springer, Berlin 1987.
2.Jean-Francois Le Gall: Mouvement brownien, martingales et calcul stochastique, Springer(2013)
3. L.C.G.Rogers and D. Williams: Diffusions, Markov processes and martingales: Ito calculus. Cambridge University Press(2000)
 


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