Linear stochastic differential equations and Wick products |
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Authors: | R Buckdahn D Nualart |
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Institution: | (1) Fachbereich Mathematik, Humboldt Universität, Postfach 1297, D-10099 Berlin, Germany;(2) Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, E-08007 Barcelona, Spain |
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Abstract: | Summary We establish the existence and uniqueness of the solution to a multidimensional linear Skorohod stochastic differential equation with deterministic diffusion matrix, using the notions of Wick product andStransform. If the diffusion matrix is constant and has real eigenvalues, the solution is a stochastic process with moments of all orders, provided that the initial condition is differentiable up to a suitable order. The case of a diffusion matrix in the first Wiener chaos is discussed in the last section.Supported by the Deutsche Forschungsgemeninschaft/Heisenberg ProgrammSupported by the DGICYT grant PB 90-0452 |
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Keywords: | 60H10 60H07 |
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