## Stochastic differential equations: an introduction with applications |

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#### Review: Stochastic Differential Equations: An Introduction with Applications

User Review - Yan Zhu - GoodreadsIt's a very well written book, but to appreciate this book, one still need a good understanding of graduate level probability knowledge, such as martingale, stopping time. I took out of 1 star after i ... Read full review

#### Review: Stochastic Differential Equations: An Introduction with Applications

User Review - Jerzy - Goodreads(supposed to be one of the best intros to stochastic calculus out there) Read full review

### Contents

lNTRODUCTlON | 1 |

SOME MATHEMATlCAL PRELlMlNARlES | 7 |

lTO lNTEGRALS | 15 |

Copyright | |

11 other sections not shown

### Common terms and phrases

1-dimensional Brownian motion a-algebra assume Borel set Chapter characteristic operator choose constant continuous function convergence Corollary define DEFINITION denotes deterministic Dirichlet problem distribution dXfc Dynkin's formula estimate EX[f(Xt EX[S example exists exit EZ[f(ZT functions f g(X ds given hand side Hence independent infinitesimal Ito diffusion Ito integral Ito interpretation Ito's formula Ju(y Kolmogorov's Lemma Let f linear filtering problem majorant of g Markov control Markov process Markov property martingale mathematical matrix measurable function normal observations obtain operator 01 optimal control optimal reward optimal stopping optimal stopping problem Poisson problem probability law Proof prove random variable result reward function satisfies solution solve Springer-Verlag stochastic control problem stochastic differential equation stochastic integral stochastic process Stratonovich strong Markov property superharmonic supermeanvalued Suppose t-continuous Theorem 5.5 theory uniqueness white noise X-harmonic