8 papers · 1 filter
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…
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…