Weak Convergence of Probability Measures of Trotter–Kato Approximate Solutions of Stochastic Evolution Equations

2020 ◽  
pp. 441-456
Author(s):  
T. E. Govindan
Keyword(s):  
Weak Convergence ◽  
Evolution Equations ◽  
Approximate Solutions ◽  
Probability Measures ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Convergence Of Probability Measures

scholarly journals Fractional Measure-dependent Nonlinear Second-order Stochastic Evolution Equations with Poisson Jumps

2018 ◽  
Vol 5 (1) ◽  
pp. 59-75 ◽  
Author(s):  
Mark A. McKibben ◽  
Micah Webster
Keyword(s):  
Evolution Equations ◽  
Mild Solutions ◽  
Stability Result ◽  
Growth Conditions ◽  
Second Order ◽  
Probability Measures ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Poisson Jumps ◽  
Fractional Measure

Abstract This paper focuses on a nonlinear second-order stochastic evolution equations driven by a fractional Brownian motion (fBm) with Poisson jumps and which is dependent upon a family of probability measures. The global existence of mild solutions is established under various growth conditions, and a related stability result is discussed. An example is presented to illustrate the applicability of the theory.

scholarly journals On a Class of Measure-Dependent Stochastic Evolution Equations Driven by fBm

2007 ◽  
Vol 2007 ◽  
pp. 1-26 ◽  
Author(s):  
Eduardo Hernandez ◽  
David N. Keck ◽  
Mark A. McKibben
Keyword(s):  
Hilbert Space ◽  
Brownian Motion ◽  
Existence And Uniqueness ◽  
Continuous Dependence ◽  
Evolution Equations ◽  
Separable Hilbert Space ◽  
Probability Measures ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Real Separable Hilbert Space

We investigate a class of abstract stochastic evolution equations driven by a fractional Brownian motion (fBm) dependent upon a family of probability measures in a real separable Hilbert space. We establish the existence and uniqueness of a mild solution, a continuous dependence estimate, and various convergence and approximation results. Finally, the analysis of three examples is provided to illustrate the applicability of the general theory.

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