Hölder Continuity of the Solution for a Class of Nonlinear SPDE Arising from One Dimensional Superprocesses

2011/05/07 by Yaozhong Hu, Fei Lu, Hu, Yaozhong +3
Economics, Econometrics and Finance · Mathematics · #60H07 60H15(35R60) 60H30 #Analysis of PDEs (math.AP) #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.AP #math.PR #msc:60H07 #msc:60H30

paper · pdf · doi:10.48550/arxiv.1105.1480

17 pages

arxiv created 2011/05/07 · openalex publication_date 2011/05/07 · arxiv updated 2011/05/10 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

The Hölder continuity of the solution to a nonlinear stochastic partial differential equation arising from one dimensional super process is obtained. It is proved that the Hölder exponent in time variable is as close as to 1/4, improving the result of 1/10 in a recent paper by Li et al [3]. The method is to use the Malliavin calculus. The Hölder continuity in spatial variable x of exponent 1/2 is also obtained by using this new approach. This Hölder continuity result is sharp since the corresponding linear heat equation has the same Hölder continuity.

Related

• Hölder regularity for a class of nonlinear stochastic heat equations
• Hölder continuity of the solutions to a class of SPDEs arising from multidimensional superprocesses in random environment
• Hölder-continuity for the nonlinear stochastic heat equation with rough initial conditions
• Improved Hölder continuity near the boundary of one-dimensional super-Brownian motion
• Joint Hölder continuity of local time for a class of interacting branching measure valued diffusions