Related papers: Martingale representations for diffusion processes…

Recently, diffusion probabilistic models (DPMs) have achieved promising results in diverse generative tasks. A typical DPM framework includes a forward process that gradually diffuses the data distribution and a reverse process that…

Ordinary differential equations obtained as limits of Markov processes appear in many settings. They may arise by scaling large systems, or by averaging rapidly fluctuating systems, or in systems involving multiple time-scales, by a…

We consider an open model possessing a Markovian quantum stochastic limit and derive the limit stochastic Schrodinger equations for the wave function conditioned on indirect observations using only the von Neumann projection postulate. We…

A multitype Dawson-Watanabe process is conditioned, in subcritical and critical cases, on non-extinction in the remote future. On every finite time interval, its distribution is absolutely continuous with respect to the law of the…

In this work, we show that for the martingale problem for a class of degenerate diffusions with bounded continuous drift and diffusion coefficients, the small noise limit of non-degenerate approximations leads to a unique Feller limit. The…

The martingale method is used to establish concentration inequalities for a class of dependent random sequences on a countable state space, with the constants in the inequalities expressed in terms of certain mixing coefficients. Along the…

We develop and implement new probabilistic strategy for proving exponential ergodicity for interacting diffusion processes on unbounded lattice. The concept of the solution used is rather weak as we construct the process in infinite…

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…

We consider a diffusion processes $\{ X_t \}$ on an interval in the natural scale. Some results are known under which $\{ X_t \}$ is a martingale, and we give simple and analytic proofs for them.

Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…

Using martingale theory, we compute, in very few lines, exact analytical expressions for various first-exit-time statistics associated with one-dimensional biased diffusion. Examples include the distribution for the first-exit time from an…

We consider the problem of finding a real valued martingale fitting specified marginal distributions. For this to be possible, the marginals must be increasing in the convex order and have constant mean. We show that, under the extra…

In [8], asymptotic expansion of the martingale with mixed normal limit was provided. The expansion formula is expressed by the adjoint of a random symbol with coefficients described by the Malliavin calculus, differently from the standard…

Novel hidden thermodynamic structures have recently been uncovered during the investigation of nonequilibrium thermodynamics for multiscale stochastic processes. Here we reveal the martingale structure for a general thermodynamic functional…

We exhibit conditions under which the flow of marginal distributions of a discontinuous semimartingale $\xi$ can be matched by a Markov process, whose infinitesimal generator is expressed in terms of the local characteristics of $\xi$. Our…

We prove a central limit theorem for a random field generated by d commuting probability preserving transformations; the martingale is given by a commuting filtration (cf. D. Khosnevisan, Multiparameter Processes, Springer 2002). The result…

The orbital angular momentum conservation of light reveals different diffraction patterns univocally dependent on the topological charge of the incident light beam when passing through a triangular aperture. It is demonstrated that these…

This paper derives physically meaningful boundary conditions for fractional diffusion equations, using a mass balance approach. Numerical solutions are presented, and theoretical properties are reviewed, including well-posedness and steady…

In this paper we introduce the concept of conic martingales}. This class refers to stochastic processes having the martingale property, but that evolve within given (possibly time-dependent) boundaries. We first review some results about…

We present Wideband Back-Projection Diffusion, an end-to-end probabilistic framework for approximating the posterior distribution induced by the inverse scattering map from wideband scattering data. This framework produces highly accurate…