New regularity results and long time behavior of pathwise (stochastic) Hamilton-Jacobi equations

2019/09/10 by Pierre‐Louis Lions, Pierre-Louis Lions, Panagiotis E. Souganidis +2
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #35D40 #60H15 #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Risk and Portfolio Optimization #Stochastic processes and financial applications #math.AP #msc:35D40 #msc:60H15

paper · pdf · doi:10.48550/arxiv.1909.05672

arXiv admin note: text overlap with arXiv:1809.01748

arxiv created 2019/09/10 · openalex publication_date 2019/09/10 · arxiv updated 2019/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present two new sharp regularity results (regularizing effect and propagation of regularity) for viscosity solutions of uniformly convex space homogeneous Hamilton-Jacobi equations. In turn, these estimates yield new intermittent stochastic regularization results for pathwise (stochastic) viscosity solutions of Hamilton-Jacobi equations with uniformly convex Hamiltonians and rough multiplicative time dependence. Finally, we use the intermittent estimates to study the long time behavior of the pathwise (stochastic) viscosity solutions of convex Hamilton-Jacobi equations.

Citations

• Pathwise solutions for fully nonlinear first- and second-order partial differential equations with multiplicative rough time dependence

Related

• Long-time behaviour of stochastic Hamilton-Jacobi equations
• Asymptotic Lipschitz regularity of viscosity solutions of Hamilton-Jacobi equations
• Homogenization of Hamilton-Jacobi equations with rough time dependence
• Speed of propagation for Hamilton-Jacobi equations with multiplicative rough time dependence and convex Hamiltonians
• Hölder regularity of Hamilton-Jacobi equations with stochastic forcing