相关论文: A general martingale approach to large noise homog…

We consider a two-dimensional weakly dissipative dynamical system with time-periodic drift and diffusion coefficients. The average of the drift is governed by a degenerate Hamiltonian whose set of critical points has an interior. The…

The goal of the paper is to describe the large time behaviour of a Markov process associated with a symmetric diffusion in a high-contrast random environment and to characterize the limit semigroup and the limit process under the diffusive…

In the strong noise regime, we study the homogeneization of quantum trajectories i.e. stochastic processes appearing in the context of quantum measurement. When the generator of the average semi-group can be separated into three distinct…

We construct a family of self-similar Markov martingales with given marginal distributions. This construction uses the self-similarity and Markov property of a reference process to produce a family of Markov processes that possess the same…

A recent paper of Melbourne & Stuart, A note on diffusion limits of chaotic skew product flows, Nonlinearity 24 (2011) 1361-1367, gives a rigorous proof of convergence of a fast-slow deterministic system to a stochastic differential…

In a quantum (inhomogeneous) Markov process $\rho_1:=\Gamma_1(\rho)$, $\rho_2:=\Gamma_1(\rho_1)$, ..., where $\Gamma_i$ are CPTP maps and $\rho$ is the initial state, the the state of the system is either oscillatory or convergent to a…

This work is devoted to deriving small mass limiting equation for a class of Hamiltonian systems with multiplicative L\'evy noise. Derivation of the limiting equation depends on the structure of the stochastic Hamiltonian systems, in which…

We use the abstract method of (local) martingale problems in order to give criteria for convergence of stochastic processes. Extending previous notions, the formulation we use is neither restricted to Markov processes (or semimartingales),…

We study the problem of homogenization for inertial particles moving in a time dependent random velocity field and subject to molecular diffusion. We show that, under appropriate assumptions on the velocity field, the large--scale,…

Typical generative diffusion models rely on a Gaussian diffusion process for training the backward transformations, which can then be used to generate samples from Gaussian noise. However, real world data often takes place in discrete-state…

Denoising diffusion probabilistic models and score-matching models have proven to be very powerful for generative tasks. While these approaches have also been applied to the generation of discrete graphs, they have, so far, relied on…

In this article, it is proved that for any cumulative distribution function with compact support and a specified t > 0, there exists a diffusion martingale which has this law at time t. The article proves existence; no claims are made about…

Under continuity and recurrence assumptions, we prove that the iteration of successive partial symmetrizations that form a time-homogeneous Markov process, converges to a symmetrization. We cover several settings, including the…

Denoising diffusions are state-of-the-art generative models exhibiting remarkable empirical performance. They work by diffusing the data distribution into a Gaussian distribution and then learning to reverse this noising process to obtain…

We show the relation between processes which are modeled by a Langevin equation with multiplicative noise and infinite ergodic theory. We concentrate on a spatially dependent diffusion coefficient that behaves as ${D(x)}\sim…

Starting from the forward and backward infinitesimal generators of bilateral, time-homogeneous Markov processes, the self-adjoint Hamiltonians of the generalized Schroedinger equations are first introduced by means of suitable Doob…

We introduce a reversible Markovian coagulation-fragmentation process on the set of partitions of $\{1,\ldots,L\}$ into disjoint intervals. Each interval can either split or merge with one of its two neighbors. The invariant measure can be…

In this paper, we study homogenization problem for strong Markov processes on $\R^d$ having infinitesimal generators $$ \sL f(x)=\int_{\R^d}\left(f(x+z)-f(x)-\langle \nabla f(x), z\rangle \I_{\{|z|\le 1\}} \right) k(x,z)\, \Pi (dz) +\langle…

The existence of global-in-time bounded martingale solutions to a general class of cross-diffusion systems with multiplicative Stratonovich noise is proved. The equations describe multicomponent systems from physics or biology with…

In Monte-Carlo methods the Markov processes used to sample a given target distribution usually satisfy detailed balance, i.e. they are time-reversible. However, relatively recent results have demonstrated that appropriate reversible and…