Results 41 to 50 of about 4,822,972 (81)

Heat equation with a general stochastic measure on nested fractals

, 2012
A stochastic heat equation on an unbounded nested fractal driven by a general stochastic measure is investigated. Existence, uniqueness and continuity of the mild solution are proved provided that the spectral dimension of the fractal is less than 4/3 ...
Radchenko, Vadym, Zähle, Martina
core   +1 more source

Remarks on non-linear noise excitability of some stochastic heat equations

, 2014
We consider nonlinear parabolic SPDEs of the form $\partial_t u=\Delta u + \lambda \sigma(u)\dot w$ on the interval $(0, L)$, where $\dot w$ denotes space-time white noise, $\sigma$ is Lipschitz continuous.
Foondun, Mohammud, Joseph, Mathew
core   +1 more source

On the multifractal local behavior of parabolic stochastic PDEs

, 2017
Consider the stochastic heat equation $\dot{u}=\frac12 u"+\sigma(u)\xi$ on $(0\,,\infty)\times\mathbb{R}$ subject to $u(0)\equiv1$, where $\sigma:\mathbb{R}\to\mathbb{R}$ is a Lipschitz (local) function that does not vanish at $1$, and $\xi$ denotes ...
Huang, Jingyu, Khoshnevisan, Davar
core   +1 more source

Strong disorder implies strong localization for directed polymers in a random environment [PDF]

, 2006
In this note we show that in any dimension $d$, the strong disorder property implies the strong localization property. This is established for a continuous time model of directed polymers in a random environment : the parabolic Anderson Model.Comment ...
Carmona, Philippe, Hu, Yueyun
core   +4 more sources

Absolute continuity for SPDEs with irregular fundamental solution

, 2014
For the class of stochastic partial differential equations studied in [Conus-Dalang,2008], we prove the existence of density of the probability law of the solution at a given point $(t,x)$, and that the density belongs to some Besov space.
Sanz-Solé, Marta, Süß, André
core   +1 more source

Some properties for superprocess under a stochastic flow

, 2006
For a superprocess under a stochastic flow, we prove that it has a density with respect to the Lebesgue measure for d=1 and is singular for d>1. For d=1, a stochastic partial differential equation is derived for the density.
Lee, Kijung, Mueller, Carl, Xiong, Jei
core   +1 more source

On L_p- theory for stochastic parabolic integro-differential equations [PDF]

, 2010
The existence and uniqueness in fractional Sobolev spaces of the Cauchy problem to a stochastic parabolic integro-differential equation is investigated. A model problem with coefficients independent of space variable is considered. The equation arises, for example, in a filtering problem with a jump signal and jump observation process.
arxiv   +1 more source

A note on intermittency for the fractional heat equation [PDF]

, 2013
The goal of the present note is to study intermittency properties for the solution to the fractional heat equation $$\frac{\partial u}{\partial t}(t,x) = -(-\Delta)^{\beta/2} u(t,x) + u(t,x)\dot{W}(t,x), \quad t>0,x \in \bR^d$$ with initial condition ...
Balan, Raluca, Conus, Daniel
core   +1 more source

An It\=o formula in the space of tempered distributions

, 2014
We extend the It\=o formula \cite{MR1837298}*{Theorem 2.3} for semimartingales with rcll paths. We also comment on Local time process of such semimartingales.
Bhar, Suprio
core   +1 more source

Model problem for integro-differential Zakai equation with discontinuous observation processes in Hölder spaces [PDF]

arXiv, 2010
The existence and uniqueness of solutions of the Cauchy problem to a a stochastic parabolic integro-differential equation is investigated. The equattion considered arises in nonlinear filtering problem with a jump signal process and jump observation.
arxiv