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 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 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.

scholarly journals Regularity, Asymptotic Solutions and Travelling Waves analysis in a porous medium system to model the interaction between invasive and invaded species

2021 ◽  
Author(s):  
José Díaz ◽  
Antonio Naranjo
Keyword(s):  
Porous Medium ◽  
Travelling Waves ◽  
Stationary Solutions ◽  
Uniqueness Of Solutions ◽  
Linear Diffusion ◽  
Diffusion Parameters ◽  
Medium System ◽  
Topological Argument ◽  
And Diffusion ◽  
Stable Connection

This work provides an analytical approach to characterize and determine solutions to a porous medium system of equations with views in applications to invasive-invaded biological dynamics. Firstly, the existence and uniqueness of solutions are proved. Afterwards, profiles of solutions are obtained making use of the selfsimilar structure that permits to show the existence of a diffusive front. The solutions are then studied within the Travelling Waves (TW) domain showing the existence of potential and exponential profiles in the stable connection that converges to the stationary solutions in which the invasive specie predominates. The TW profiles are shown to exist based on the geometry perturbation theory together with an analytical-topological argument in the phase plane. The finding of an exponential decaying rate (related with the advection and diffusion parameters) in the invaded specie TW is not trivial in the non-linear diffusion case and reflects the existence of a TW trajectory governed by the invaded specie runaway (in the direction of the advection) and the diffusion (acting along a finite speed front or support).

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.

scholarly journals Dynkin’s Isomorphism Theorem and the Stochastic Heat Equation

2010 ◽  
Vol 34 (3) ◽  
pp. 243-260
Author(s):  
Nathalie Eisenbaum ◽  
Mohammud Foondun ◽  
Davar Khoshnevisan
Keyword(s):  
Heat Equation ◽  
Stochastic Heat Equation ◽  
Isomorphism Theorem ◽  
The Stochastic Heat Equation
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