7 papers
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…
On Uniqueness and Blowup Properties for a Class of Second Order SDEs
Alejandro Gomez, Jong Jun Lee, Carl Mueller +2
As the first step for approaching the uniqueness and blowup properties of the solutions of the stochastic wave equations with multiplicative noise, we analyze the conditions for th…