On pathwise uniqueness for stochastic heat equations with non-Lipschitz coefficients
Copyright policy )On pathwise uniqueness for stochastic heat equations with non-Lipschitz coefficients
We consider the existence and pathwise uniqueness of the stochastic heat equation with a multiplicative colored noise term on IR^d for d greater or equal to 1. We focus on the case of non-Lipschitz noise coefficients and singular spatial noise correlations. In the course of the proof a new result on Hoelder continuity of the solutions near zero is established.
39 pages
- University of British Columbia Canada
- Technion – Israel Institute of Technology Israel
- University of Delaware United States
- University of Göttingen Germany
Heat equation colored noise stochastic partial differential equation uniqueness existence, 60K35 Secondary 60K37, 510, Stochastic partial differential equations (aspects of stochastic analysis), 60F05, Branching processes (Galton-Watson, birth-and-death, etc.), FOS: Mathematics, Processes in random environments, 60J80, 60H15; 60K35, Heat equation, Probability (math.PR), existence, uniqueness, Interacting random processes; statistical mechanics type models; percolation theory, Central limit and other weak theorems, stochastic partial differential equation, 60K37, colored noise, 60K35, stochastic partial ddifferential equation, 60H15, AMS: Primary 60H15, Mathematics - Probability
Heat equation colored noise stochastic partial differential equation uniqueness existence, 60K35 Secondary 60K37, 510, Stochastic partial differential equations (aspects of stochastic analysis), 60F05, Branching processes (Galton-Watson, birth-and-death, etc.), FOS: Mathematics, Processes in random environments, 60J80, 60H15; 60K35, Heat equation, Probability (math.PR), existence, uniqueness, Interacting random processes; statistical mechanics type models; percolation theory, Central limit and other weak theorems, stochastic partial differential equation, 60K37, colored noise, 60K35, stochastic partial ddifferential equation, 60H15, AMS: Primary 60H15, Mathematics - Probability
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