Transcription of Tutorial on Stochastic Di erential Equations - johnboccio.com
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Tutorial on Stochastic Di erential Equations - johnboccio.com
Please cite as J. R. Movellan (2011) Tutorial on Stochastic Differential Equations ,MPLab Tutorials Version on Stochastic DifferentialEquationsJavier R. MovellanCopyrightc 2003, 2004, 2005, 2006, Javier R. MovellanThis document is being reorganized. Expect redundancy, inconsistencies, disorga-nized presentation ..1 MotivationThere is a wide range of interesting processes in robotics, control, economics, thatcan be described as a differential Equations with non-deterministic dynamics. Sup-pose the original processes is described by the following differential equationdXtdt=a(Xt)(1)with initial conditionX0, which could be random. We wish to construct a math-ematical model of how the may behave in the presence of noise.
Brownian motion sample paths are non-di erentiable with probability 1 This is the basic why we need to develop a generalization of ordinary calculus to handle stochastic di erential equations.
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