Related papers: A solution selection problem with small symmetric …
In this work we consider solutions to stochastic partial differential equations with transport noise, which are known to converge, in a suitable scaling limit, to solution of the corresponding deterministic PDE with an additional viscosity…
It is shown that a well-known theory of random stationary processes contain contradictions. Integral representations of correlation functions and random stationary processes are investigated further. The new method of struggle with…
The purpose of the article is to address the limiting behavior of the solutions of stochastic differential equations driven by a pointy $d$-dimensional gradient as the intensity of the underlying Brownian motion tends to $0$. By pointy…
We analyze the strong noise limit of one-dimensional stochastic differential equations (SDEs). Our initial motivation comes from continuous measurements of open quantum systems. In this context, Bauer, Bernard and Tilloy pointed out an…
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…
Motivated by problems from statistical analysis for discretely sampled SPDEs, first we derive central limit theorems for higher order finite differences applied to stochastic process with arbitrary finitely regular paths. These results are…
Pathwise uniqueness for stochastic PDEs with drift in differential form is a main open problem in the recent literature on regularisation by noise. This paper establishes a self-contained theory in the framework of stochastic evolution…
The goal of the paper is to analytically examine escape probabilities for dynamical systems driven by symmetric $\alpha$-stable L\'evy motions. Since escape probabilities are solutions of a type of integro-differential equations (i.e.,…
We consider a slow passage through a point of loss of stability. If the passage is sufficiently slow, the dynamics are controlled by additive random disturbances, even if they are extremely small. We derive expressions for the `exit value'…
We introduce a variational method for analyzing limit cycle oscillators in $\mathbb{R}^d$ driven by Gaussian noise. This allows us to derive exact stochastic differential equations (SDEs) for the amplitude and phase of the solution, which…
Estimating parameters of drift and diffusion coefficients for multidimensional stochastic delay equations with small noise are considered. The delay structure is written as an integral form with respect to a delay measure. Our contrast…
The technique of stochastic solutions, previously used for deterministic equations, is here proposed as a solution method for partial differential equations driven by distribution-valued noises.
Dynamical system models with delayed dynamics and small noise arise in a variety of applications in science and engineering. In many applications, stable equilibrium or periodic behavior is critical to a well functioning system. Sufficient…
In this paper, we study a class of stochastic partial differential equations (SPDEs) driven by space-time fractional noises. Our method consists in studying first the nonlocal SPDEs and showing then the convergence of the family of these…
We show that perturbing ill-posed differential equations with (potentially very) smooth random processes can restore well-posedness -- even if the perturbation is (potentially much) more regular than the drift component of the solution. The…
We consider stochastic dynamical systems defined by differential equations with a uniform random time delay. The latter equations are shown to be equivalent to deterministic higher-order differential equations: for an $n$-th order equation…
This work focuses on the regularization by nonlinear noise for a class of partial differential equations that may only have local solutions. In particular, we obtain the global existence, uniqueness and the Feller property for stochastic 3D…
We study the statistical properties of stochastic evolution equations driven by space-only noise, either additive or multiplicative. While forward problems, such as existence, uniqueness, and regularity of the solution, for such equations…
We study a stochastic differential equation with an unbounded drift and general H\"older continuous noise of an arbitrary order. The corresponding equation turns out to have a unique solution that, depending on a particular shape of the…
The current series of papers is concerned with stochastic stability of monotone dynamical systems by identifying the basic dynamical units that can survive in the presence of noise interference. In the first of the series, for the…