Related papers: A Kolmogorov type theorem for stochastic fields

Multifractal analysis of stochastic processes deals with the fine scale properties of the sample paths and seeks for some global scaling property that would enable extracting the so-called spectrum of singularities. In this paper we…

We present the general framework of \'Ecalle's moulds in the case of linearization of a formal vector field without and within resonances. We enlighten the power of moulds by their universality, and calculability. We modify then \'Ecalle's…

On the one hand, we investigate the existence and pathwise uniqueness of a nonnegative martingale solution to the stochastic evolution system of nonlinear advection-diffusion equations proposed by Klausmeier with Gaussian multiplicative…

In many applications, the common assumption that a driving noise process affecting a system is independent or Markovian may not be realistic, but the noise process may be assumed to be stationary. To study such problems, this paper…

While Kolmogorov's probability axioms are widely recognized, it is less well known that in an often-overlooked 1930 note, Kolmogorov proposed an axiomatic framework for a unifying concept of the mean -- referred to as regular means. This…

We present a generalized linear response theory for mixed jump-diffusion models -- combining Gaussian and L\'evy noise interacting with nonlinear dynamics -- by deriving comprehensive response formulas accounting for perturbations to both…

We study the logarithmic conformal field theories in which conformal weights are continuous subset of real numbers. A general relation between the correlators consisting of logarithmic fields and those consisting of ordinary conformal…

In this article we discuss a version of the Chebotarev density for function fields over perfect fields with procyclic absolute Galois groups. Our version of this density theorem differs from other versions in two aspects: we include…

We provide new regularity results for the solutions of the Kolmogorov equation associated to a SPDE with nonlinear diffusion coefficients and a Burgers type nonlinearity. This generalizes previous results in the simpler cases of additive or…

Kolmogorov's invariant torus theorem is proved using a simple fixed point theorem.

A general variational principle of classical fields with a Lagrangian containing the field quantity and its derivatives of up to the N-th order is presented. Noether's theorem is derived. The generalized Hamilton-Jacobi's equation for the…

We consider a stochastic model of incompressible non-Newtonian fluids of second grade on a bounded domain of $\mathbb{R}^2$ driven by L\'evy noise. Applying the variational approach, global existence and uniqueness of strong probabilistic…

We provide a sufficient condition for the continuity of real valued permanental processes. When applied to the subclass of permanental processes which consists of squares of Gaussian processes, we obtain the sufficient condition for…

In this paper, we use a unified framework to study Poisson stable (including stationary, periodic, quasi-periodic, almost periodic, almost automorphic, Birkhoff recurrent, almost recurrent in the sense of Bebutov, Levitan almost periodic,…

We present a systematic treatment of non-Gaussianity in stochastic systems using the Schwinger-Keldysh effective field theory framework, in which the non-Gaussianity is realized as nonlinear terms in the fluctuation field. We establish two…

We prove the existence and the Besov regularity of the density of the solution to a general parabolic SPDE which includes the stochastic Burgers equation on an unbounded domain. We use an elementary approach based on the fractional…

In this paper, new conditions for the stability of V-geometrically ergodic Markov chains are introduced. The results are based on an extension of the standard perturbation theory formulated by Keller and Liverani. The continuity and higher…

We set up a generalization of ubiquitous one-parameter families in algebraic geometry and their use for stability theories ([GIT, HL, AHLH]) to families over toric varieties and their analytic analogues. The language allows us to…

For stochastic conservation laws driven by a semilinear noise term, we propose a generalization of the Kru\v{z}kov entropy condition by allowing the Kru\v{z}kov constants to be Malliavin differentiable random variables. Existence and…

In this paper, we study the Besov regularity of L\'evy white noises on the $d$-dimensional torus. Due to their rough sample paths, the white noises that we consider are defined as generalized stochastic fields. We, initially, obtain…