scholarly journals S-asymptotically w-periodic solutions in the p-th mean for a Stochastic Evolution Equation driven by Q-Brownian motion

2017 ◽  
Vol 2 (5) ◽  
pp. 124-133 ◽  
Author(s):  
Solym Mawaki Manou-Abi ◽  
William Dimbour
Keyword(s):  
Brownian Motion ◽  
Evolution Equation ◽  
Periodic Solutions ◽  
Stochastic Evolution Equation ◽  
Stochastic Evolution

Moderate deviation for parameter estimator in the stochastic parabolic equations with additive fractional Brownian motion

2014 ◽  
Vol 14 (03) ◽  
pp. 1450002
Author(s):  
Jiang Hui
Keyword(s):  
Brownian Motion ◽  
Evolution Equation ◽  
Fractional Brownian Motion ◽  
Parabolic Equations ◽  
Moderate Deviation ◽  
Hurst Parameter ◽  
Stochastic Evolution Equation ◽  
Stochastic Evolution ◽  
Parameter Estimator ◽  
Asymptotic Behaviors

In this paper, we study the asymptotic behaviors of parameter estimator in a diagonalizable stochastic evolution equation driven by additive fractional Brownian motion with Hurst parameter H ∈ [½, 1). The moderate deviation for this estimator can be obtained.

A FILTERING PROBLEM FOR A LINEAR STOCHASTIC EVOLUTION EQUATION DRIVEN BY A FRACTIONAL BROWNIAN MOTION

2008 ◽  
Vol 08 (03) ◽  
pp. 397-412
Author(s):  
WILFRIED GRECKSCH ◽  
CONSTANTIN TUDOR
Keyword(s):  
Brownian Motion ◽  
Evolution Equation ◽  
Fractional Brownian Motion ◽  
Solution Process ◽  
Innovation Process ◽  
Optimal Estimation ◽  
Stochastic Evolution Equation ◽  
Stochastic Evolution ◽  
Finite Dimensional ◽  
Observation Process

A linear unbiased and square mean optimal estimation is obtained for the mild solution process of a stochastic evolution equation with an infinite-dimensional fractional Brownian motion as noise and the noise in the observation process is a finite-dimensional Brownian motion. An innovation process is introduced and the estimation is obtained as a solution of a stochastic differential equation with a finite-dimensional noise. By using an approach based on the equivalence with a deterministic control problem, the estimation for the Fourier coefficients of the signal process is also determined.

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.

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