We provide a stochastic representation for a general class of viscous Hamilton-Jacobi (HJ) equations, which has convex and superlinear nonlinearity in its gradient term, via a type of backward stochastic differential equation (BSDE) with constraint in the martingale part. We compare our result with the classical representation in terms of (super)quadratic BSDEs, and show in particular that existence of a viscosity solution to the viscous HJ equation can be obtained under more general growth assumptions on the coefficients, including both unbounded diffusion coefficient and terminal data.

Cosso, A., Pham, H., Xing, H. (2017). BSDEs with diffusion constraint and viscous Hamilton–Jacobi equations with unbounded data. ANNALES DE L'INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 53(4), 1528-1547 [10.1214/16-AIHP762].

BSDEs with diffusion constraint and viscous Hamilton–Jacobi equations with unbounded data

Cosso, Andrea;
2017

Abstract

We provide a stochastic representation for a general class of viscous Hamilton-Jacobi (HJ) equations, which has convex and superlinear nonlinearity in its gradient term, via a type of backward stochastic differential equation (BSDE) with constraint in the martingale part. We compare our result with the classical representation in terms of (super)quadratic BSDEs, and show in particular that existence of a viscosity solution to the viscous HJ equation can be obtained under more general growth assumptions on the coefficients, including both unbounded diffusion coefficient and terminal data.
2017
Cosso, A., Pham, H., Xing, H. (2017). BSDEs with diffusion constraint and viscous Hamilton–Jacobi equations with unbounded data. ANNALES DE L'INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 53(4), 1528-1547 [10.1214/16-AIHP762].
Cosso, Andrea; Pham, Huyên; Xing, Hao
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/610967
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