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