BSDEs with diffusion constraint and viscous Hamilton-Jacobi equations with unbounded data
Probability
2017-03-09 v2
Abstract
We provide a stochastic representation for a general class of viscous Hamilton-Jacobi (HJ) equations, which has convexity 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 BSDE, and show in particular that existence of a 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.
Keywords
Cite
@article{arxiv.1505.06868,
title = {BSDEs with diffusion constraint and viscous Hamilton-Jacobi equations with unbounded data},
author = {Andrea Cosso and Huyên Pham and Hao Xing},
journal= {arXiv preprint arXiv:1505.06868},
year = {2017}
}
Comments
to appear in Annales de l'Institut Henri Poincar{\'e} (B), Probabilit{\'e}s et statistique