相关论文: Duals and inverse flows of generalized Ornstein-Uh…

In the paper we consider models of generalized counting processes time-changed by a general inverse subordinator, we characterize their distributions and present governing equations for them. The equations are given in terms of the…

We introduce the notion of time reversal in open quantum systems as represented by linear quantum operations, and a related generalization of classical entropy production in the environment. This functional is the ratio of the probability…

Active Ornstein-Uhlenbeck particles (AOUPs) are overdamped particles in an interaction potential subject to external Ornstein-Uhlenbeck noises. They can be transformed into a system of underdamped particles under additional velocity…

In this paper, we study the stochastic Hamiltonian flow in Wasserstein manifold, the probability density space equipped with $L^2$-Wasserstein metric tensor, via the Wong--Zakai approximation. We begin our investigation by showing that the…

The paper is concerned with one-dimensional two-sided Ornstein-Uhlenbeck type processes with delay or anticipation. We prove existence and uniqueness requiring almost sure boundedness on the left half-axis in case of delay and almost sure…

We show that anomalous diffusion arises in two different models for the motion of randomly forced and weakly damped particles: one is a generalisation of the Ornstein-Uhlenbeck process with a random force which depends on position as well…

We consider the problem of leakage or effusion of an ensemble of independent stochastic processes from a region where they are initially randomly distributed. The case of Brownian motion, initially confined to the left half line with…

We give new and explicitly computable examples of Gibbs-non-Gibbs transitions of mean-field type, using the large deviation approach introduced in [4]. These examples include Brownian motion with small variance and related diffusion…

We derive renormalised finite functional flow equations for quantum field theories in real and imaginary time that incorporate scale transformations of the renormalisation conditions, hence implementing a flowing renormalisation. The flows…

The Malliavin derivative, divergence operator, and the Ornstein-Uhlenbeck operator are extended from the traditional Gaussian setting to generalized processes from the higher-order chaos spaces.

We obtain the tail probability of generalized sub-Gaussian canonical processes. It can be viewed as a variant of the Bernstein-type inequality in the i.i.d case, and we further get a tighter bound of concentration inequality through…

New generalized equations of motion for the Weber-Clebsch potentials that describe both the Navier-Stokes and MHD dynamics are derived. These depend on a new parameter, which has dimensions of time for Navier-Stokes and inverse velocity for…

We obtain stochastic duality functions for specific Markov processes using representation theory of Lie algebras. The duality functions come from the kernel of a unitary intertwiner between $*$-representations, which provides (generalized)…

Stochastic processes are proposed whose master equations coincide with classical wave, telegraph, and Klein-Gordon equations. Similar to predecessors based on the Goldstein-Kac telegraph process, the model describes the motion of particles…

Using a continuous unitary transformation recently proposed by Wegner \cite{Wegner} together with an approximation that neglects irrelevant contributions, we obtain flow equations for Hamiltonians. These flow equations yield a diagonal or…

Frequently observed divergence of numerical solutions to benchmark flows of the UCM viscoelastic fluid is a known and widely discussed issue. Some authors consider such singularities "invincible". The article argues this position, to which…

It is shown that the Truncated Euler Equations, i.e. a finite set of ordinary differential equations for the amplitude of the large-scale modes, can correctly describe the complex transitional dynamics that occur within the turbulent regime…

Regression on function spaces is typically limited to models with Gaussian process priors. We introduce the notion of universal functional regression, in which we aim to learn a prior distribution over non-Gaussian function spaces that…

Several integrate-to-threshold models with differing temporal integration mechanisms have been proposed to describe the accumulation of sensory evidence to a prescribed level prior to motor response in perceptual decision-making tasks. An…

A set of exact integrals of motion is found for systems driven by homogenous isotropic stochastic flow. The integrals of motion describe the evolution of (hyper-)surfaces of different dimensions transported by the flow, and can be expressed…