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Uniqueness and non-uniqueness of solutions of Vlasov-McKean equations

Part of: Equations and systems with randomness Stochastic analysis

Published online by Cambridge University Press:  09 April 2009

Michael Scheutzow
Michael Scheutzow
Affiliation:
Fachbereich MathematikUniversität KaiserslauternD-6750 Kaiserslautern West, Germany
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Abstract

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We study the equation dY(t)/dt = f(Y(t), Eh(Y(t))) for random initial conditions, where E denotes the expected value. It turns out that in contrast to the deterministic case local Lipschitz continuity of f and h are not sufficient to ensure uniqueness of the solutions. Finally we also state some sufficient conditions for uniqueness.

MSC classification

Secondary: 34F05: Equations and systems with randomness 60H10: Stochastic ordinary differential equations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 43 , Issue 2 , October 1987 , pp. 246 - 256
Copyright
Copyright © Australian Mathematical Society 1987

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