Forward-backward stochastic equations associated with systems of quasilinear parabolic equations and comparison theorems

DOI10.1007/s10958-014-2183-6zbMath1359.60077OpenAlexW1989711777MaRDI QIDQ906002

Yana I. Belopolskaya

Publication date: 28 January 2016

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-014-2183-6

zbMATH Keywords

quasilinear parabolic equationsviscosity solutionsforward-backward stochastic differential equations

Mathematics Subject Classification ID

Applications of stochastic analysis (to PDEs, etc.) (60H30) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Initial value problems for second-order parabolic systems (35K45) Viscosity solutions to PDEs (35D40) Comparison principles in context of PDEs (35B51)

Related Items (3)

Probabilistic model for the Lotka-Volterra system with cross-diffusion ⋮ Probabilistic representations and numerical algorithms for classical and viscosity solutions of the Cauchy problem for quasilinear parabolic systems ⋮ Probabilistic models of the conservation and balance laws in switching regimes

Cites Work

• Probabilistic approach to viscosity solutions of the Cauchy problems for systems if fully nonlinear parabolic equations
• Multi-dimensional reflected backward stochastic differential equations and the comparison theorem
• Probabilistic interpretation of a system of semilinear parabolic partial differential equations
• On the comparison theorem for multidimensional BSDEs
• Second-order backward stochastic differential equations and fully nonlinear parabolic PDEs
• Functional Integration and Partial Differential Equations. (AM-109)
• Probabilistic interpretation for systems of quasilinear parabolic partial differential equations
• User’s guide to viscosity solutions of second order partial differential equations
• On certain systems of parabolic equations
• FUNCTIONAL INTEGRALS CONNECTED WITH OPERATOR EVOLUTION EQUATIONS
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