Stochastic heat equation with piecewise constant coefficients and generalized fractional type noise

2021 ◽  
Vol 104 ◽  
pp. 123-144
Author(s):  
M. Zili ◽  
E. Zougar
Keyword(s):  
Heat Equation ◽  
Stochastic Heat Equation ◽  
Piecewise Constant ◽  
Constant Coefficients ◽  
Fractional Type

scholarly journals Fractional stochastic heat equation with piecewise constant coefficients

2020 ◽  
Vol 21 (01) ◽  
pp. 2150002
Author(s):  
Yuliya Mishura ◽  
Kostiantyn Ralchenko ◽  
Mounir Zili ◽  
Eya Zougar
Keyword(s):  
Diffusion Coefficient ◽  
Heat Equation ◽  
Divergence Form ◽  
Stochastic Heat Equation ◽  
Piecewise Constant ◽  
Constant Diffusion Coefficient ◽  
Infinite Dimensional ◽  
Order Elliptic Operator ◽  
Constant Diffusion ◽  
Constant Coefficients

We introduce a fractional stochastic heat equation with second-order elliptic operator in divergence form, having a piecewise constant diffusion coefficient, and driven by an infinite-dimensional fractional Brownian motion. We characterize the fundamental solution of its deterministic part, and prove the existence and the uniqueness of its solution.

scholarly journals Quadratic covariations for the solution to a stochastic heat equation with space-time white noise

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xichao Sun ◽  
Litan Yan ◽  
Xianye Yu
Keyword(s):  
Heat Equation ◽  
White Noise ◽  
Space Time ◽  
Stochastic Heat Equation

scholarly journals Spatial Moduli of Non-Differentiability for Linearized Kuramoto–Sivashinsky SPDEs and Their Gradient

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1251
Author(s):  
Wensheng Wang
Keyword(s):  
Heat Equation ◽  
White Noise ◽  
Fourth Order ◽  
Gaussian Processes ◽  
Three Dimensional ◽  
Space Time ◽  
Symmetry Analysis ◽  
Stochastic Heat Equation ◽  
Moduli Of Continuity

We investigate spatial moduli of non-differentiability for the fourth-order linearized Kuramoto–Sivashinsky (L-KS) SPDEs and their gradient, driven by the space-time white noise in one-to-three dimensional spaces. We use the underlying explicit kernels and symmetry analysis, yielding spatial moduli of non-differentiability for L-KS SPDEs and their gradient. This work builds on the recent works on delicate analysis of regularities of general Gaussian processes and stochastic heat equation driven by space-time white noise. Moreover, it builds on and complements Allouba and Xiao’s earlier works on spatial uniform and local moduli of continuity of L-KS SPDEs and their gradient.

Optimal control of backward stochastic heat equation with Neumann boundary control and noise

Stochastics ◽  
2012 ◽  
Vol 85 (3) ◽  
pp. 532-558 ◽  
Author(s):  
Huaiqiang Yu ◽  
Bin Liu
Keyword(s):  
Optimal Control ◽  
Heat Equation ◽  
Boundary Control ◽  
Neumann Boundary ◽  
Stochastic Heat Equation

Estimation of the Hurst and diffusion parameters in fractional stochastic heat equation

2021 ◽  
Vol 104 ◽  
pp. 61-76
Author(s):  
D. A. Avetisian ◽  
K. V. Ralchenko
Keyword(s):  
Heat Equation ◽  
Stochastic Heat Equation ◽  
Diffusion Parameters ◽  
And Diffusion

scholarly journals A weak convergence approach to hybrid LQG problems with infinite control weights

2002 ◽  
Vol 15 (1) ◽  
pp. 1-21
Author(s):  
G. George Yin ◽  
Jiongmin Yong
Keyword(s):  
Markov Chain ◽  
Weak Convergence ◽  
Small Parameter ◽  
Limit Problem ◽  
Discrete Events ◽  
Linear Quadratic ◽  
Piecewise Constant ◽  
Constant Coefficients ◽  
The Cost ◽  
Random Times

This work is concerned with a class of hybrid LQG (linear quadratic Gaussian) regulator problems modulated by continuous-time Markov chains. In contrast to the traditional LQG models, the systems have both continuous dynamics and discrete events. In lieu of a model with constant coefficients, these coefficients vary with time and exhibit piecewise constant behavior. At any time t, the system follows a stochastic differential equation in which the coefficients take one of the m possible configurations where m is usually large. The system may jump to any of the possible configurations at random times. Further, the control weight in the cost functional is allowed to be indefinite. To reduce the complexity, the Markov chain is formulated as singularly perturbed with a small parameter. Our effort is devoted to solving the limit problem when the small parameter tends to zero via the framework of weak convergence. Although the limit system is still modulated by a Markov chain, it has a much smaller state space and thus, much reduced complexity.

scholarly journals Moderate deviations for a fractional stochastic heat equation with spatially correlated noise

2017 ◽  
Vol 17 (04) ◽  
pp. 1750025 ◽  
Author(s):  
Yumeng Li ◽  
Ran Wang ◽  
Nian Yao ◽  
Shuguang Zhang
Keyword(s):  
Heat Equation ◽  
Moderate Deviation ◽  
Stochastic Heat Equation ◽  
Correlated Noise ◽  
Derivative Operator ◽  
Spatially Correlated ◽  
Whole Space ◽  
Convergence Method ◽  
Spatially Correlated Noise ◽  
Weak Convergence Method

In this paper, we study the Moderate Deviation Principle for a perturbed stochastic heat equation in the whole space [Formula: see text]. This equation is driven by a Gaussian noise, white in time and correlated in space, and the differential operator is a fractional derivative operator. The weak convergence method plays an important role.

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