Related papers: Gaussian integrability of distance function under …

This work is devoted to almost sure and moment exponential stability of regime-switching jump diffusions. The Lyapunov function method is used to derive sufficient conditions for stabilities for general nonlinear systems; which further…

Certain extremum estimators have asymptotic distributions that are non-Gaussian, yet characterizable as the distribution of the $\argmax$ of a Gaussian process. This paper presents high-level sufficient conditions under which such…

We investigate an example of noise-induced stabilization in the plane that was also considered in (Gawedzki, Herzog, Wehr 2010) and (Birrell, Herzog, Wehr 2011). We show that despite the deterministic system not being globally stable, the…

In this paper, we answer the question about the criteria of existence of monotone travelling fronts $u = \phi(\nu \cdot x+ct), \phi(-\infty) =0, \phi(+\infty) = \kappa,$ for the monostable (and, in general, non-quasi-monotone) delayed…

A moderate deviation principle for nonlinear functions of Gaussian processes is established. The nonlinear functions need not be locally bounded. Especially, the logarithm is allowed. (Thus, small deviations of the process are relevant.)…

We prove a converse Lyapunov theorem for boundedness of reachability sets for a general class of control systems whose flow is Lipschitz continuous on compact intervals with respect to trajectory-dominated inputs. We show that this…

This article considers a class of metastable non-reversible diffusion processes whose invariant measure is a Gibbs measure associated with a Morse potential. In a companion paper [32], we proved the Eyring-Kramers formula for the…

The Gaussian integral, denoted as \( \int_{-\infty}^{\infty} e^{-x^2} dx \), plays a significant role in mathematical literature. In this paper, we explore a family of integrals related to Gaussian functions. Specifically, we introduce…

Let G={G(x), x\in R_+}, G(0)=0, be a mean zero Gaussian process with $E(G(x)-G(y))^2=\sigma ^2(x-y) $. Let $ \rho (x)= \frac12{d^{2}\over dx^2}\sigma^2(x)$, $x\ne 0 $. When $\rho^{k}$ is integrable at zero and satisfies some additional…

In this paper we present an integro-differential diffusion equation for continuous time random walk that is valid for a generic waiting time probability density function. Using this equation we also study diffusion behaviors for a couple of…

We consider infinitely divisible distributions with symmetric L\'evy measure and study the absolute continuity of them with respect to the Lebesgue measure. We prove that if $\eta(r)=\int_{|x|\le r} x^2 \nu(dx)$ where $\nu$ is the L\'evy…

In this article, we study the smallest distances between the zeros of Gaussian analytic functions over compact Riemann surfaces. Our main result is that, after appropriate rescaling, the point process of the smallest distances converge to a…

We consider infinite-dimensional diffusions where the interaction between the coordinates has a finite extent both in space and time. In particular, it is not supposed to be smooth or Markov. The initial state of the system is Gibbs, given…

This paper is devoted to improvements of functional inequalities based on scalings and written in terms of relative entropies. When scales are taken into account and second moments fixed accordingly, deficit functionals provide explicit…

We prove a robust converse barrier function theorem via the converse Lyapunov theory. While the use of a Lyapunov function as a barrier function is straightforward, the existence of a converse Lyapunov function as a barrier function for a…

We give a criterion of the form Q(d)c(M)<1 for the non-reconstructability of tree-indexed q-state Markov chains obtained by broadcasting a signal from the root with a given transition matrix M. Here c(M) is an explicit function, which is…

We consider reversible diffusions in random environment and prove the Einstein relation for this model. It says that the derivative of the effective velocity under an additional local drift equals the diffusivity of the model without drift.…

Although the spatially continuous version of the reaction-diffusion equation has been well studied, in some instances a spatially-discretized representation provides a more realistic approximation of biological processes. Indeed,…

Let $\mu$ be a self-affine measure on $\mathbb{R}^{d}$ associated to an affine IFS $\Phi$ and a positive probability vector $p$. Suppose that the maps in $\Phi$ do not have a common fixed point, and that standard irreducibility and…

This paper provides a precise error analysis for the maximum likelihood estimate $\hat{a}_{\text{ML}}(u_1^n)$ of the parameter $a$ given samples $u_1^n = (u_1, \ldots, u_n)'$ drawn from a nonstationary Gauss-Markov process $U_i = a U_{i-1}…