A THEOREM DUAL TO YAMADA–WATANABE THEOREM FOR STOCHASTIC EVOLUTION EQUATIONS

2010 ◽  
Vol 10 (03) ◽  
pp. 367-374 ◽  
Author(s):  
HUIJIE QIAO
Keyword(s):  
Evolution Equation ◽  
Strong Solution ◽  
Existence And Uniqueness ◽  
Variational Approach ◽  
Evolution Equations ◽  
Stochastic Evolution Equation ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Uniqueness In Law ◽  
Strong Existence

In this paper, we prove that uniqueness in law and strong existence for a stochastic evolution equation [Formula: see text] imply existence and uniqueness of a strong solution in the framework of the variational approach. This result seems to be dual to Yamada–Watanabe theorem in [7].

scholarly journals An Inverse Problem for a Class of Linear Stochastic Evolution Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-25
Author(s):  
Yuhuan Zhao
Keyword(s):  
Inverse Problem ◽  
Evolution Equation ◽  
Evolution Equations ◽  
Optimal Parameter ◽  
Optimization Method ◽  
Necessary Condition ◽  
Stochastic Evolution Equation ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Fréchet Differentiable

An inverse problem for a linear stochastic evolution equation is researched. The stochastic evolution equation contains a parameter with values in a Hilbert space. The solution of the evolution equation depends continuously on the parameter and is Fréchet differentiable with respect to the parameter. An optimization method is provided to estimate the parameter. A sufficient condition to ensure the existence of an optimal parameter is presented, and a necessary condition that the optimal parameter, if it exists, should satisfy is also presented. Finally, two examples are given to show the applications of the above results.

scholarly journals On Jumps Stochastic Evolution Equations With Application of Homogenization and Large Deviations

2019 ◽  
Vol 11 (2) ◽  
pp. 125
Author(s):  
Cl´ement Manga ◽  
Alioune Coulibaly ◽  
Alassane Diedhiou
Keyword(s):  
Evolution Equation ◽  
Large Deviations ◽  
Evolution Equations ◽  
Stochastic Evolution Equation ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Large Deviations Principle ◽  
Viscosity Parameter ◽  
Two Parameters ◽  
And Diffusion

We consider a class of jumps and diffusion stochastic differential equations which are perturbed by to two parameters:  ε (viscosity parameter) and δ (homogenization parameter) both tending to zero. We analyse the problem taking into account the combinatorial effects of the two parameters  ε and δ . We prove a Large Deviations Principle estimate for jumps stochastic evolution equation in case that homogenization dominates.

scholarly journals Integrated solutions of stochastic evolution equations with additive noise

2001 ◽  
Vol 64 (2) ◽  
pp. 281-290 ◽  
Author(s):  
A. Filinkov ◽  
I. Maizurna
Keyword(s):  
Evolution Equation ◽  
Additive Noise ◽  
Evolution Equations ◽  
Stochastic Evolution Equation ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Existence Of A Solution ◽  
Integrated Semigroup

We investigate the existence of a solution to the abstract stochastic evolution equation with additive noise: in the case when A is the generator of an n-times integrated semigroup.

scholarly journals Weak pullback mean random attractors for stochastic evolution equations and applications

2021 ◽  
pp. 2240001
Author(s):  
Anhui Gu
Keyword(s):  
Stochastic Models ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Random Attractors ◽  
Porous Media Equations ◽  
Stochastic Reaction

In this paper, we investigate the existence and uniqueness of weak pullback mean random attractors for abstract stochastic evolution equations with general diffusion terms in Bochner spaces. As applications, the existence and uniqueness of weak pullback mean random attractors for some stochastic models such as stochastic reaction–diffusion equations, the stochastic [Formula: see text]-Laplace equation and stochastic porous media equations are established.

scholarly journals A UNIFIED EXISTENCE AND UNIQUENESS THEOREM FOR STOCHASTIC EVOLUTION EQUATIONS

2009 ◽  
Vol 81 (1) ◽  
pp. 33-46
Author(s):  
A. JENTZEN ◽  
P. E. KLOEDEN
Keyword(s):  
Diffusion Coefficient ◽  
Uniqueness Theorem ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Trace Class ◽  
Existence And Uniqueness Theorem ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Class Noise

AbstractAn existence and uniqueness theorem for mild solutions of stochastic evolution equations is presented and proved. The diffusion coefficient is handled in a unified way which allows a unified theorem to be formulated for different cases, in particular, of multiplicative space–time white noise and trace-class noise.

scholarly journals Existence and Uniqueness of Solutions for Delay Stochastic Evolution Equations of Second Order in Time

2003 ◽  
Vol 03 (02) ◽  
pp. 141-167 ◽  
Author(s):  
María J. Garrido-Atienza ◽  
José Real
Keyword(s):  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Second Order ◽  
Point Of View ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Uniqueness Of Solutions ◽  
Second Order In Time ◽  
Functional Setting

Some results on the existence and uniqueness of solutions for stochastic evolution equations of second order in time, containing some hereditary characteristics, are proved. Our theory is developed from a variational point of view and in a general functional setting which permit us to deal with several kinds of delay terms in a unified formulation. The theory is illustrated with two examples.

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