On the existence of universal functional solutions to classical SDE's

On the existence of universal functional solutions to classical SDE's

Olav Kallenberg

Source: Ann. Probab. Volume 24, Number 1 (1996), 196-205.

Abstract

Assume that the weak existence and pathwise uniqueness hold for solutions to the equation $dX_t=\sigma(t,X)dB_t + b(t,X)dt$ starting at fixed points. then there exists a Borel measurable function F, such that any solution (X,B) satisfies $X = F(X_0,B)$ a.s. This strengthens a fundamental result of Yamada and Watanbe, where F may depend on the initial distribution $\mu$

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Primary Subjects: 60H10

Secondary Subjects: 60G44

Keywords: Weak and strong solutions; pathwise uniqueness; local martingale problem

Full-text: Open access

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aop/1042644713
Mathematical Reviews number (MathSciNet): MR1387632
Digital Object Identifier: doi:10.1214/aop/1042644713
Zentralblatt MATH identifier: 0861.60070

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References

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YAMADA, T. and WATANABE, S. 1971. On the uniqueness of solutions of stochastic differential equations. J. Math. Ky oto Univ. 11 155 167.

Zentralblatt MATH: 0236.60037

Mathematical Reviews (MathSciNet): MR278420

Project Euclid: euclid.kjm/1250523691

AUBURN, ALABAMA 36849-5310 E-mail: clark@mail.auburn.edu

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