A partial differential equation with the white noise as a coefficient

1973 ◽  
Vol 28 (1) ◽  
pp. 53-71 ◽  
Author(s):  
Shigeyoshi Ogawa
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
White Noise ◽  
Partial Differential

Composition and invariance methods for solving some stochastic control problems

1975 ◽  
Vol 7 (02) ◽  
pp. 299-329 ◽  
Author(s):  
V. E. Beneš
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Dynamical Systems ◽  
White Noise ◽  
Stochastic Control ◽  
Analytical Methods ◽  
Control Problems ◽  
Numerical Treatment ◽  
Partial Differential ◽  
Stochastic Control Problems

This paper considers certain stochastic control problems in which control affects the criterion through the process trajectory. Special analytical methods are developed to solve such problems for certain dynamical systems forced by white noise. It is found that some control problems hitherto approachable only through laborious numerical treatment of the non-linear Bellman-Hamilton-Jacobi partial differential equation can now be solved.

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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