6 citations · 12 across the 27 of their papers we have counts for
34 papers
Uniform large deviation principles for the stochastic heat equation over unbounded sets of initial data
Michael Salins, Esmée Theewis
We study small-noise large deviations for the stochastic heat equation (SHE) on the torus with unbounded, multiplicative space-time white noise. We establish uniform large deviatio…
Positive probability of explosion for stochastic heat equation with superlinear accretive reaction term and polynomially growing multiplicative noise
Michael Salins, Yuyang Zhang
This paper studies the finite time explosion of the stochastic heat equation $\frac{\partial u}{\partial t}(t,x)=\frac{\partial^2}{\partial x^2} u(t,x)+(u(t,x))^β+σ(u(t,x))\dot{W}(…
Global in time solutions to stochastic reaction-diffusion systems with superlinear reactions satisfying a triangular control of mass
Dionysis Milesis, Michael Salins
We study systems of reaction-diffusion equations perturbed by multiplicative noise, where the reaction terms satisfy quasipositivity, a triangular mass-control structure, and polyn…
Gaussian fluctuations for the nonlinear stochastic heat equation with drift
Raluca M. Balan, Michael Salins
In this article, we prove the Quantitative Central Limit Theorem (QCLT) for the spatial average of the solution of the nonlinear stochastic heat equation with constant initial cond…
Nonexplosion for a large class of superlinear stochastic parabolic equations, in arbitrary spatial dimension
Michael Salins, Yuyang Zhang
This paper explores the finite time explosion of the stochastic parabolic equation in arbitrary bounded spatial d…
Uniform attraction and exit problems for stochastic damped wave equations
Ioannis Gasteratos, Michael Salins, Konstantinos Spiliopoulos
We consider a class of wave equations with constant damping and polynomial nonlinearities that are perturbed by small, multiplicative, space-time white noise. The equations are def…
Global solutions to the stochastic heat equation with superlinear accretive reaction term and polynomially growing multiplicative noise
Michael Salins
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 assum…
Preventing Finite-Time Blowup in a Constrained Potential for Reaction-Diffusion Equations
John Ivanhoe, Michael Salins
We examine stochastic reaction-diffusion equations of the form and provide sufficient condi…
Global solution for superlinear stochastic heat equation on under Osgood-type conditions
Le Chen, Mohammud Foondun, Jingyu Huang +1
We study the \textit{stochastic heat equation} (SHE) on subject to a centered Gaussian noise that is white in time and colored in space.The drift term is assumed to satisfy…
Solutions to the stochastic heat equation with polynomially growing multiplicative noise do not explode in the critical regime
Michael Salins
We investigate the finite time explosion of the stochastic heat equation in the critical setting where grows l…
Regularity of the law of solutions to the stochastic heat equation with non-Lipschitz reaction term
Michael Salins, Samy Tindel
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-Lipsc…
Importance sampling for stochastic reaction-diffusion equations in the moderate deviation regime
Ioannis Gasteratos, Michael Salins, Konstantinos Spiliopoulos
We develop a provably efficient importance sampling scheme that estimates exit probabilities of solutions to small-noise stochastic reaction-diffusion equations from scaled neighbo…
Global solutions to the stochastic heat equation with superlinear accretive reaction term and superlinear multiplicative noise term on a bounded spatial domain
Michael Salins
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.…
Global solutions for the stochastic reaction-diffusion equation with super-linear multiplicative noise and strong dissipativity
Michael Salins
A condition is identified that implies that solutions to the stochastic reaction-diffusion equation on a bound…
Existence and uniqueness of global solutions to the stochastic heat equation with super-linear drift on an unbounded spatial domain
Michael Salins
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 s…
Moderate deviations for systems of slow-fast stochastic reaction-diffusion equations
Ioannis Gasteratos, Michael Salins, Konstantinos Spiliopoulos
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 comp…
Systems of small-noise stochastic reaction-diffusion equations satisfy a large deviations principle that is uniform over all initial data
Michael Salins
Large deviations principles characterize the exponential decay rates of the probabilities of rare events. Cerrai and Rockner [13] proved that systems of stochastic reaction-diffusi…
Existence and uniqueness for the mild solution of the stochastic heat equation with non-Lipschitz drift on an unbounded spatial domain
Michael Salins
We prove the existence and uniqueness of the mild solution for a nonlinear stochastic heat equation defined on an unbounded spatial domain. The nonlinearity is not assumed to be gl…
An improved uniqueness result for a system of stochastic differential equations related to the stochastic wave equation
C. Mueller, E. Neuman, M. Salins +1
We improve on the strong uniqueness results of [GLM+17], which deal with the following system of SDE. \begin{align*} dX_t&=Y_tdt \\ dY_t&=|X_{t}|^αdB_t \end{align*} and $X_0=x_0,Y_…
Metastability and exit problems for systems of stochastic reaction-diffusion equations
Michael Salins, Konstantinos Spiliopoulos
In this paper we develop a metastability theory for a class of stochastic reaction-diffusion equations exposed to small multiplicative noise. We consider the case where the unpertu…
Uniform large deviation principles for Banach space valued stochastic differential equations
Amarjit Budhiraja, Paul Dupuis, Michael Salins
We prove a large deviation principle (LDP) for a general class of Banach space valued stochastic differential equations (SDE) that is uniform with respect to initial conditions in…
Smoluchowski-Kramers approximation for the damped stochastic wave equation with multiplicative noise in any spatial dimension
Michael Salins
We show that the solutions to the damped stochastic wave equation converge pathwise to the solution of a stochastic heat equation. This is called the Smoluchowski-Kramers approxima…
Equivalences and counterexamples between several definitions of the uniform large deviations principle
Michael Salins
This paper explores the equivalences between four definitions of uniform large deviations principles and uniform Laplace principles found in the literature. Counterexamples are pre…
Large deviations and averaging for systems of slow--fast stochastic reaction--diffusion equations
Wenqing Hu, Michael Salins, Konstantinos Spiliopoulos
We study a large deviation principle for a system of stochastic reaction--diffusion equations (SRDEs) with a separation of fast and slow components and small noise in the slow comp…