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Skorohod stochastic differential equations of diffusion type
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  • Published: September 1992

Skorohod stochastic differential equations of diffusion type

  • Rainer Buckdahn1 

Probability Theory and Related Fields volume 93, pages 297–323 (1992)Cite this article

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Summary

Leta, b beC 2(R 1)-functions with bounded derivatives of first and second order. We study stochastic differential equations

$$dX_t = a(X_t )dW_t + b(X_t )dt,0 \leqq t \leqq 1,$$

whose initial valueX 0 is a Fréchet differentiable random variable which may depend on the whole path of the driving Brownian motion (W t ). This anticipation requires to pass from the Itô-integral to the Skorohod-integral. We show that the equation has a unique local solution {X t (ω), 0≦t≦t 0(ω)}, for sufficiently smallt 0(ω)>0, and we provide conditions for the existence of a global solution {X t (ω), 0≦t≦1}.

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Authors and Affiliations

  1. Fachbereich Mathematik, Humboldt-Universität, Unter den Linden 6, O-1086, Berlin, Federal Republic of Germany

    Rainer Buckdahn

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  1. Rainer Buckdahn
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Buckdahn, R. Skorohod stochastic differential equations of diffusion type. Probab. Th. Rel. Fields 93, 297–323 (1992). https://doi.org/10.1007/BF01193054

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  • Received: 03 May 1991

  • Revised: 04 February 1992

  • Issue Date: September 1992

  • DOI: https://doi.org/10.1007/BF01193054

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  • 60H15
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