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Probabilistic interpretation for a system of quasilinear parabolic partial differential equation combined with algebra equations

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  • Wu, Zhen
  • Yu, Zhiyong

Abstract

In this paper, we study a kind of system of second order quasilinear parabolic partial differential equation combined with algebra equations. Introducing a family of coupled forward–backward stochastic differential equations, and by virtue of some delicate analysis techniques, we give a probabilistic interpretation for it in the viscosity sense.

Suggested Citation

  • Wu, Zhen & Yu, Zhiyong, 2014. "Probabilistic interpretation for a system of quasilinear parabolic partial differential equation combined with algebra equations," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 3921-3947.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:12:p:3921-3947
    DOI: 10.1016/j.spa.2014.07.013
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    Cited by:

    1. Chen, Xin & Ye, Wenjie, 2021. "A probabilistic representation for heat flow of harmonic map on manifolds with time-dependent Riemannian metric," Statistics & Probability Letters, Elsevier, vol. 177(C).

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