Stochastic IntegralsAmerican Mathematical Soc., 1969 - 141 sidor The AMS is excited to bring this volume, originally published in 1969, back into print. This well-written book has been used for many years to learn about stochastic integrals. The author starts with the presentation of Brownian motion, then deals with stochastic integrals and differentials, including the famous Ito lemma. The rest of the book is devoted to various topics of stochastic integral equations and stochastic integral equations on smooth manifolds. E. B. Dynkin wrote aboutthe original edition in Mathematical Reviews: "This little book is a brilliant introduction to an important boundary field between the theory of probability and that of differential equations ... differential and integral calculus based upon Brownian motion." These words continue to ring true today.This classic book is ideal for supplementary reading or independent study. It is suitable for graduate students and researchers interested in probability, stochastic processes, and their applications. |
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1-dimensional Brownian motion 2t lg₂ B₁ B₂ begins afresh belongs to C[(0 Bessel process Borel-Cantelli lemma Brownian motion run Brownian path Brownian stopping C(R¹ coefficients compact completes the proof compute constant continuous function convergent sum coordinates D₁ db)² Define diffusion disk E[exp e₁ e₂ e² ds eigenvalue elementary solution elliptic operator equation explosion fact Feller's test follows formula governed by G grad implies independent indicator function Itô Itô-McKean Itô's lemma j₁ j₂ manifold martingale martingale inequality max b(s nonanticipating Brownian functional nonanticipating functional nonanticipating solution nonnegative nonsingular oblique reflection P[max Plim Problem prove reader Riemann surface Section 2.9 simple solution of du/dt solution of dx Step stochastic differential stochastic differential equation stochastic integral submartingale t₁ t¹(t t₂ verify Weyl's lemma x₁
Hänvisningar till den här boken
Brownian Motion and Stochastic Calculus Ioannis Karatzas,Steven Shreve Begränsad förhandsgranskning - 1991 |
Stochastic Flows and Stochastic Differential Equations Hiroshi Kunita,H. Kunita Begränsad förhandsgranskning - 1990 |