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Linear stochastic differential equations and Wick products
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  • Published: December 1994

Linear stochastic differential equations and Wick products

  • R. Buckdahn1,2 &
  • D. Nualart1,2 

Probability Theory and Related Fields volume 99, pages 501–526 (1994)Cite this article

  • 298 Accesses

  • 20 Citations

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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.

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Author information

Authors and Affiliations

  1. Fachbereich Mathematik, Humboldt Universität, Postfach 1297, D-10099, Berlin, Germany

    R. Buckdahn & D. Nualart

  2. Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, E-08007, Barcelona, Spain

    R. Buckdahn & D. Nualart

Authors
  1. R. Buckdahn
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  2. D. Nualart
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Additional information

Supported by the Deutsche Forschungsgemeninschaft/Heisenberg Programm

Supported by the DGICYT grant PB 90-0452

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Cite this article

Buckdahn, R., Nualart, D. Linear stochastic differential equations and Wick products. Probab. Th. Rel. Fields 99, 501–526 (1994). https://doi.org/10.1007/BF01206230

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  • Received: 03 January 1994

  • Revised: 14 February 1994

  • Issue Date: December 1994

  • DOI: https://doi.org/10.1007/BF01206230

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Mathematics Subject Classification

  • 60H10
  • 60H07
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