Small Perturbation of Stochastic Parabolic Equations: A Power Series Analysis

“…Some relevant interesting work have recently been undertaken, mainly for parabolic SPDEs; see for instance [3,8,10,11,21,43,44]. We also note the closely related work [3,25,15,16] dealing with stochastic homogenization for SPDEs with small parameters. The list of references is of course not exhaustive, but a representation of the main trends in the field.…”

mentioning

confidence: 95%

Homogenization of nonlinear hyperbolic stochastic partial differential equations with nonlinear damping and forcing

Mohammed¹,

Sango²

2019

Networks &Amp; Heterogeneous Media

View full text Add to dashboard Cite

In this paper we deal with the homogenization of stochastic nonlinear hyperbolic equations with periodically oscillating coefficients involving nonlinear damping and forcing driven by a multi-dimensional Wiener process. Using the two-scale convergence method and crucial probabilistic compactness results due to Prokhorov and Skorokhod, we show that the sequence of solutions of the original problem converges in suitable topologies to the solution of a homogenized problem, which is a nonlinear damped stochastic hyperbolic partial differential equation. More importantly, we also prove the convergence of the associated energies and establish a crucial corrector result.

show abstract

“…With the use of the Kushner‐Stratonovich equation, the whole filtering problem is theoretically solved. Some computational methods to solve this equation are discussed in .…”

Section: Introductionmentioning

confidence: 99%

Modal Kalman Filter

Mohammaddadi

Pariz

Karimpour

2016

Asian Journal of Control

View full text Add to dashboard Cite

In the Extended Kalman Filter (EKF), only the first‐order term of the Taylor series is employed. Hence, the nonlinearities in the system dynamics are not fully considered. In the proposed method, to overcome this drawback, the higher‐order terms of the Taylor series are considered and a new filter, based on the Modal series, is designed. In this paper, based on the Modal series and careful approximations, a nonlinear filter is converted to a series of linear filters, and the extracted filter is named the Modal Kalman Filter (MKF). The efficiency and advantage of MKF are analytically proven and its applicability examined with some simulations.

show abstract

Small Perturbation of Stochastic Parabolic Equations: A Power Series Analysis

Cited by 6 publications

References 25 publications

An Asymptotic Comparison of Two Time-Homogeneous PAM Models

An Asymptotic Comparison of Two Time-Homogeneous PAM Models

Homogenization of nonlinear hyperbolic stochastic partial differential equations with nonlinear damping and forcing

Modal Kalman Filter

Contact Info

Product

Resources

About