Boundary behavior and interior Hölder regularity of the solution to nonlinear stochastic partial differential equation driven by space-time white noise

2020 ◽  
Vol 269 (11) ◽  
pp. 9904-9935
Author(s):  
Beom-Seok Han ◽  
Kyeong-Hun Kim
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
White Noise ◽  
Stochastic Partial Differential Equation ◽  
Boundary Behavior ◽  
Space Time ◽  
Hölder Regularity ◽  
Partial Differential ◽  
Holder Regularity

A DEGENERATE STOCHASTIC PARTIAL DIFFERENTIAL EQUATION FOR THE PURELY ATOMIC SUPERPROCESS WITH DEPENDENT SPATIAL MOTION

2003 ◽  
Vol 06 (04) ◽  
pp. 597-607 ◽  
Author(s):  
DONALD A. DAWSON ◽  
ZENGHU LI ◽  
HAO WANG
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
White Noise ◽  
Unique Solution ◽  
Stochastic Partial Differential Equation ◽  
Spatial Motion ◽  
Partial Differential ◽  
Brownian Motions ◽  
Time Space ◽  
Dependent Spatial Motion

A purely atomic superprocess with dependent spatial motion is characterized as the pathwise unique solution of a stochastic partial differential equation, which is driven by a time-space white noise defining the spatial motion and a sequence of independent Brownian motions defining the branching mechanism.

THE STOCHASTIC MAGNETO-HYDRODYNAMIC SYSTEM

1999 ◽  
Vol 02 (02) ◽  
pp. 241-265 ◽  
Author(s):  
S. S. SRITHARAN ◽  
P. SUNDAR
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
White Noise ◽  
Stochastic Partial Differential Equation ◽  
Martingale Problem ◽  
Partial Differential ◽  
Hydrodynamic System ◽  
Well Posed

The magneto-hydrodynamic system perturbed by white noise is cast as a stochastic partial differential equation taking values in an appropriate Lusin space. The martingale problem associated with this SPDE is shown to be well-posed under suitable conditions.

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