Related papers: Exponential ergodicity and Rayleigh-Schroedinger s…

The 1/[-i\omega + D(\omega, q)q^2] diffusion pole in the localized phase transfers to the 1/\omega Berezinskii-Gorkov singularity, which can be analyzed by the instanton method (M V. Sadovskii, 1982; J. L. Cardy, 1978). Straightforward use…

We construct and study the one-parameter semigroup of $\sigma$-finite measures ${\cal L}^{\theta}$, $\theta>0$, on the space of Schwartz distributions that have an infinite-dimensional abelian group of linear symmetries; this group is a…

An approximate maximum likelihood method of estimation of diffusion parameters $(\vartheta,\sigma)$ based on discrete observations of a diffusion $X$ along fixed time-interval $[0,T]$ and Euler approximation of integrals is analyzed. We…

A finitely-additive measure $\lambda $ on an infinite-dimensional real Hilbert space $E$ which is invariant with respect to shifts and orthogonal mappings has been defined. This measure can be considered as the analog of the Lebesgue…

We establish a complete Widder Theory for the fractional fast diffusion equation. Our work focuses on nonnegative solutions satisfying a certain integral size condition at infinity. We prove that these solutions possess a Radon measure as…

This paper is concerned with the inhomogeneous incompressible Euler system. We establish a Duchon--Robert type approximation theorem for the distribution describing the local energy flux of bounded solutions. The velocity field is assumed…

We prove ergodicity for random dynamics satisfying some expansion and irreducibility conditions. As a particular application, we show that if $R_1,R_2\in \mathrm{SO}(d+1)$, $d\ge 2$, generate a dense subgroup, then the random dynamics of…

In this paper, we consider the cubic nonlinear Schr\"odinger equation with third order dispersion on the circle. In the non-resonant case, we prove that the mean-zero Gaussian measures on Sobolev spaces $H^s(\mathbb{T})$, $s > \frac 34$,…

We prove the invariance of the Gibbs measure under the dynamics of the three-dimensional cubic wave equation, which is also known as the hyperbolic $\Phi^4_3$-model. This result is the hyperbolic counterpart to seminal works on the…

In this paper a concentration inequality is proved for the deviation in the ergodic theorem in the case of discrete time observations of diffusion processes. The proof is based on the geometric ergodicity property for diffusion processes.…

Let $k \ge 1$ be an integer and $f$ a holomorphic endomorphism of $\mathbb P^k (\mathbb C)$ of algebraic degree $d\geq 2$. We introduce a volume dimension for ergodic $f$-invariant probability measures with strictly positive Lyapunov…

Let $X_t$ be a reversible and positive recurrent diffusion in $R^d$ described by \begin{equation}\nonumber X_t=x+\sigma b(t)+\int_0^tm(X_s)\dif s, \end{equation} where the diffusion coefficient $\sigma$ is a positive-definite matrix and the…

Answering the question of V.I. Oseledets, we present a random variable $\xi$ such that the sum $\xi(x)+a\xi(y)$ has a singular distribution for a set of parameters $a$ dense in $(1, +\infty)$, but for another dense set of parameters, this…

We show that every subshift factor of a ($-\beta$)-shift is intrinsically ergodic, when $\beta\geq \frac{1+\sqrt{5}}{2}$ and the ($-\beta$)-expansion of $1$ is not periodic with odd period. Moreover, the unique measure of maximal entropy…

We construct the infinitesimal generator of the Brox diffusion on a line with a periodic Brownian environment. This gives a new construction of the process and allows to solve the singular martingale problem. We prove that the associated…

The ergodic theory and geometry of the Julia set of meromorphic functions on the complex plane with polynomial Schwarzian derivative is investigated under the condition that the forward trajectory of asymptotic values in the Julia set is…

Our first purpose is to extend the results from \cite{T} on the radial defocusing NLS on the disc in $\mathbb{R}^2$ to arbitrary smooth (defocusing) nonlinearities and show the existence of a well-defined flow on the support of the Gibbs…

Given a parabolic cylinder $Q =(0,T)\times\Omega$, where $\Omega\subset \mathbb{R}^{N}$ is a bounded domain, we prove new properties of solutions of \[ u_t-\Delta_p u = \mu \quad \text{in $Q$} \] with Dirichlet boundary conditions, where…

We show that if $(X, \mu, T)$ is a probability measure-preserving dynamical system, and $\mathscr{P}$ is a countable partition of $(X, \mu)$, then the limit $$ \lim_{n, k \to \infty} \mathbb{E} \left[ \frac{1}{k} \sum_{j = 0}^{k - 1} f…

In this short article, we shall study one-dimensional local Dirichlet spaces. One result, which has its independent interest, is to prove that irreducibility implies the uniqueness of symmetrizing measure for right Markov processes. The…