Anticipating Stochastic Differential Equations of Stratonovich Type

Anticipating Stochastic Differential Equations of Stratonovich Type We prove the existence and uniqueness of Stratonovich stochastic differential equations where the coefficients and the initial condition may depend on the whole path of the driving Wiener process. Our main hypothesis is that the diffusion coefficient satisfies the Frobenius condition. The solution is given in terms of solutions of ordinary differential equations and the Wiener process. We use this representation to study properties of the solution. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Anticipating Stochastic Differential Equations of Stratonovich Type

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Publisher
Springer-Verlag
Copyright
Copyright © Inc. by 1997 Springer-Verlag New York
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s002459900063
Publisher site
See Article on Publisher Site

Abstract

We prove the existence and uniqueness of Stratonovich stochastic differential equations where the coefficients and the initial condition may depend on the whole path of the driving Wiener process. Our main hypothesis is that the diffusion coefficient satisfies the Frobenius condition. The solution is given in terms of solutions of ordinary differential equations and the Wiener process. We use this representation to study properties of the solution.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Aug 1, 2089

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