Theory of Stochastic Differential Equations with Jumps and Applications
Publication year: 2005
ISBN: 978-0-387-25175-2
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This book is written for people who are interested in stochastic differential equations (SDEs) and their applications. It shows how to introduce and define the Ito integrals, to establish Ito’s differential rule (the so-called Ito formula), to solve the SDEs, and to establish Girsanov’s theorem and obtain weak solutions of SDEs. It also shows how to solve the filtering problem, to establish the martingale representation theorem, to solve the option pricing problem in a financial market, and to obtain the famous Black-Scholes formula, along with other results.
Subject: Engineering, Brownian motion, Martingale, Stochastic calculus, Differential equation, linear Optimization, Maximum principle, Point process
