Wave equation in the plane driven by a general stochastic measure

2019 ◽  
Vol 98 ◽  
pp. 73-90 ◽  
Author(s):  
I. M. Bodnarchuk ◽  
V. M. Radchenko
Keyword(s):  
Wave Equation ◽  
Stochastic Measure ◽  
General Stochastic

scholarly journals Asymptotics of the mild solution of awave equation in three-dimensional space driven by a general stochastic measure

2019 ◽  
pp. 12-17
Author(s):  
I. M. Bodnarchuk
Keyword(s):  
Cauchy Problem ◽  
Wave Equation ◽  
Mild Solution ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Absolute Value ◽  
Stochastic Measure ◽  
The Cauchy Problem ◽  
Three Dimensional Space ◽  
General Stochastic

We study the Cauchy problem for a wave equation in three-dimensional space driven by a general stochastic measure. Under some assumptions, we prove that the mild solution tends to zero almost surely as the absolute value of the spatial variable tends to infinity.

RANDOM FIELDS: NON-ANTICIPATING DERIVATIVE AND DIFFERENTIATION FORMULAS

2007 ◽  
Vol 10 (03) ◽  
pp. 465-481 ◽  
Author(s):  
GIULIA DI NUNNO
Keyword(s):  
Random Fields ◽  
Random Variables ◽  
Space Time ◽  
Explicit Formulas ◽  
Stochastic Measure ◽  
Stochastic Derivative ◽  
Differentiation Formulas ◽  
General Stochastic

The non-anticipating stochastic derivative represents the integrand in the best L2-approximation for random variables by Itô non-anticipating integrals with respect to a general stochastic measure with independent values on a space–time product. In this paper some explicit formulas for this derivative are obtained.

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