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April, 1977 On the Existence, Uniqueness, Convergence and Explosions of Solutions of Systems of Stochastic Integral Equations
Philip E. Protter
Ann. Probab. 5(2): 243-261 (April, 1977). DOI: 10.1214/aop/1176995849

Abstract

A theory of stochastic integral equations is developed for the integrals of Kunita, Watanabe, and P. A. Meyer. Existence and uniqueness of solutions of systems of equations with semimartingale (or "quasi-martingale") differentials is proved, in which we include as particular cases the customary results as put forth by McKean and Gihman and Skorohod. Under weaker conditions we prove existence and uniqueness with explosions, and study the explosion times. We show that when the (random) coefficients or the differentials converge, the solutions converge to the solution of the limiting equation.

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Philip E. Protter. "On the Existence, Uniqueness, Convergence and Explosions of Solutions of Systems of Stochastic Integral Equations." Ann. Probab. 5 (2) 243 - 261, April, 1977. https://doi.org/10.1214/aop/1176995849

Information

Published: April, 1977
First available in Project Euclid: 19 April 2007

zbMATH: 0363.60044
MathSciNet: MR431380
Digital Object Identifier: 10.1214/aop/1176995849

Subjects:
Primary: 60H10
Secondary: 60H20

Keywords: Brownian motion , local martingales , quasi-martingales , Semimartingales , Stochastic differential equations , stochastic integrals , Wiener process

Rights: Copyright © 1977 Institute of Mathematical Statistics

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Vol.5 • No. 2 • April, 1977
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