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Stochastic Parabolic Equations of Full Second Order

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Topics in Stochastic Analysis and Nonparametric Estimation

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 145))

Abstract

A procedure is described for defining a generalized solution for stochastic differential equations using the Cameron-Martin version of the Wiener Chaos expansion. Existence and uniqueness of this Wiener Chaos solution is established for parabolic stochastic PDEs such that both the drift and the diffusion operators are of the second order.

Sergey V. Lototsky acknowledges support from NSF CAREER award DMS-0237724. Boris L. Rozovskii acknowledges support from NSF Grant DMS 0604863, ARO Grant W911NF-07-1-0044, and ONR Grant N00014-07-1-0044.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, USC, Los Angeles, CA, 90089

    Sergey V. Lototsky

  2. Division of Applied Mathematics, Brown University, Providence, RI, 02912

    Boris L. Rozovskii

Authors
  1. Sergey V. Lototsky
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  2. Boris L. Rozovskii
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Wayne State University, Detroit, MI, 48202

    Pao-Liu Chow , George Yin  & Boris Mordukhovich ,  & 

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Lototsky, S.V., Rozovskii, B.L. (2008). Stochastic Parabolic Equations of Full Second Order. In: Chow, PL., Yin, G., Mordukhovich, B. (eds) Topics in Stochastic Analysis and Nonparametric Estimation. The IMA Volumes in Mathematics and its Applications, vol 145. Springer, New York, NY. https://doi.org/10.1007/978-0-387-75111-5_9

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