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Backward SDEs and Cauchy problem for semilinear equations in divergence form
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  • Published: March 2003

Backward SDEs and Cauchy problem for semilinear equations in divergence form

  • Andrzej Rozkosz1 

Probability Theory and Related Fields volume 125, pages 393–407 (2003)Cite this article

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Abstract.

 We extend the definition of solutions of backward stochastic differential equations to the case where the driving process is a diffusion corresponding to symmetric uniformly elliptic divergence form operator. We show existence and uniqueness of solutions of such equations under natural assumptions on the data and show its connections with solutions of semilinear parabolic partial differential equations in Sobolev spaces.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland. e-mail: rozkosz@mat.uni.torun.pl, , , , , , PL

    Andrzej Rozkosz

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  1. Andrzej Rozkosz
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Additional information

Received: 22 January 2002 / Revised version: 10 September 2002 / Published online: 19 December 2002

Research supported by KBN Grant 0253 P03 2000 19.

Mathematics Subject Classification (2002): Primary 60H30; Secondary 35K55

Key words or phrases: Backward stochastic differential equation – Semilinear partial differential equation – Divergence form operator – Weak solution

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Rozkosz, A. Backward SDEs and Cauchy problem for semilinear equations in divergence form. Probab Theory Relat Fields 125, 393–407 (2003). https://doi.org/10.1007/s00440-002-0244-0

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  • Issue Date: March 2003

  • DOI: https://doi.org/10.1007/s00440-002-0244-0

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Keywords

  • Differential Equation
  • Partial Differential Equation
  • Cauchy Problem
  • Sobolev Space
  • Divergence Form
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