Stochastic Calculus: A Practical Introduction

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CRC Press, Jun 21, 1996 - Mathematics - 341 pages
This compact yet thorough text zeros in on the parts of the theory that are particularly relevant to applications . It begins with a description of Brownian motion and the associated stochastic calculus, including their relationship to partial differential equations. It solves stochastic differential equations by a variety of methods and studies in detail the one-dimensional case. The book concludes with a treatment of semigroups and generators, applying the theory of Harris chains to diffusions, and presenting a quick course in weak convergence of Markov chains to diffusions.

The presentation is unparalleled in its clarity and simplicity. Whether your students are interested in probability, analysis, differential geometry or applications in operations research, physics, finance, or the many other areas to which the subject applies, you'll find that this text brings together the material you need to effectively and efficiently impart the practical background they need.
 

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Contents

Brownian Motion
1
Stochastic Integration
33
Brownian Motion II
95
Partial Differential Equations
125
Stochastic Differential Equations
177
One Dimensional Diffusions
211
Diffusions as Markov Processes
245
Weak Convergence
271
Solutions to Exercises
311
References
335
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