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pro vyhledávání: '"Salins, Michael"'
Autor:
Salins, Michael
We prove that mild solutions to the stochastic heat equation with superlinear accretive forcing and polynomially growing multiplicative noise cannot explode under two sets of assumptions. The first set of assumptions allows both the deterministic for
Externí odkaz:
http://arxiv.org/abs/2409.15527
Autor:
Ivanhoe, John, Salins, Michael
We examine stochastic reaction-diffusion equations of the form $\frac{\partial u}{\partial t} = \mathcal{A} u(t,x) + f(u(t,x)) + \sigma(u(t,x))\dot{W}(t,x)$ and provide sufficient conditions on the reaction term and multiplicative noise term that gua
Externí odkaz:
http://arxiv.org/abs/2406.15672
We study the \textit{stochastic heat equation} (SHE) on $\R^d$ subject to a centered Gaussian noise that is white in time and colored in space.The drift term is assumed to satisfy an Osgood-type condition and the diffusion coefficient may have certai
Externí odkaz:
http://arxiv.org/abs/2310.02153
Autor:
Salins, Michael
We investigate the finite time explosion of the stochastic heat equation $\frac{\partial u}{\partial t} = \Delta u(t,x) + \sigma(u(t,x))\dot{W}(t,x)$ in the critical setting where $\sigma$ grows like $\sigma(u) \approx C(1 + |u|^\gamma)$ and $\gamma
Externí odkaz:
http://arxiv.org/abs/2309.04330
Autor:
Salins, Michael, Tindel, Samy
We prove the existence of density for the solution to the multiplicative semilinear stochastic heat equation on an unbounded spatial domain, with drift term satisfying a half-Lipschitz type condition. The methodology is based on a careful analysis of
Externí odkaz:
http://arxiv.org/abs/2302.10678
We develop a provably efficient importance sampling scheme that estimates exit probabilities of solutions to small-noise stochastic reaction-diffusion equations from scaled neighborhoods of a stable equilibrium. The moderate deviation scaling allows
Externí odkaz:
http://arxiv.org/abs/2206.00646
Autor:
Salins, Michael
We describe sufficient conditions on the reaction terms and multiplicative noise terms of a stochastic reaction-diffusion equation that guarantee that the solutions never explode. Both the reaction term and multiplicative noise terms are allowed to g
Externí odkaz:
http://arxiv.org/abs/2110.10130
Autor:
Salins, Michael
A condition is identified that implies that solutions to the stochastic reaction-diffusion equation $\frac{\partial u}{\partial t} = \mathcal{A} u + f(u) + \sigma(u) \dot{W}$ on a bounded spatial domain never explode. We consider the case where $\sig
Externí odkaz:
http://arxiv.org/abs/2107.04459
Autor:
Salins, Michael
We prove the existence and uniqueness of global solutions to the semilinear stochastic heat equation on an unbounded spatial domain with forcing terms that grow superlinearly and satisfy an Osgood condition $\int 1/|f(u)|du = +\infty$ along with addi
Externí odkaz:
http://arxiv.org/abs/2106.13221
The goal of this paper is to study the Moderate Deviation Principle (MDP) for a system of stochastic reaction-diffusion equations with a time-scale separation in slow and fast components and small noise in the slow component. Based on weak convergenc
Externí odkaz:
http://arxiv.org/abs/2101.00085