Related papers: Ito Diffusion Approximation of Universal Ito Chain…
Spatially-distributed, nonequilibrium chemical systems described by a Markov chain model are considered. The evolution of such systems arises from a combination of local birth-death reactive events and random walks executed by the particles…
In this note, we apply Transition Path Theory (TPT) from Markov chains to shed light on the problem of Iceland-Scotland Overflow Water (ISOW) equatorward export. A recent analysis of observed trajectories of submerged floats demanded…
Given a random variable $F$ regular enough in the sense of the Malliavin calculus, we are able to measure the distance between its law and almost any continuous probability law on the real line. The bounds are given in terms of the…
We prove several properties of the EMCEL scheme, which is capable of approximating one-dimensional continuous strong Markov processes in distribution on the path space (the scheme is briefly recalled). Special cases include irregular…
A stochastic incremental subgradient algorithm for the minimization of a sum of convex functions is introduced. The method sequentially uses partial subgradient information and the sequence of partial subgradients is determined by a general…
Parameter inference for stochastic differential equations is challenging due to the presence of a latent diffusion process. Working with an Euler-Maruyama discretisation for the diffusion, we use variational inference to jointly learn the…
For integer valued random variables, the translated Poisson distributions form a flexible family for approximation in total variation, in much the same way that the normal family is used for approximation in Kolmogorov distance. Using the…
Imprecise continuous-time Markov chains are a robust type of continuous-time Markov chains that allow for partially specified time-dependent parameters. Computing inferences for them requires the solution of a non-linear differential…
In the paper, we study a new rate of convergence estimate for homogeneous discrete-time nonlinear Markov chains based on the Markov-Dobrushin condition. This result generalizes the convergence estimates for any positive number of transition…
In this paper, we study small noise asymptotics of Markov-modulated diffusion processes in the regime that the modulating Markov chain is rapidly switching. We prove the joint sample-path large deviations principle for the Markov-modulated…
We propose a new approach to apply the chaining technique in conjunction with information-theoretic measures to bound the generalization error of machine learning algorithms. Different from the deterministic chaining approach based on…
In this work, a stochastic energy supply-demand model with renewable integration is developed and analyzed. The basic nonlinear deterministic model describing the relationship among regional demand, external supply, energy imports, and…
A diffusion taking value in probability measures on a graph with a vertex set $V$, $\sum_{i\in V}x_i\delta_i$, is studied. The masses on each vertices satisfy the stochastic differential equation of the form $dx_i=\sum_{j\in…
We revisit the classical problem of approximating a stochastic differential equation by a discrete-time and discrete-space Markov chain. Our construction iterates Caratheodory's theorem over time to match the moments of the increments…
We consider linearizations of stochastic differential equations with additive noise using the Karhunen-Lo\`eve expansion. We obtain our linearizations by truncating the expansion and writing the solution as a series of matrix-vector…
We study existence and uniqueness for one-dimensional generalized stochastic differential equations with singular coefficients, including distributional drift and degenerate, possibly discontinuous, diffusion coefficients. Such…
The problem of estimating an unknown discrete distribution from its samples is a fundamental tenet of statistical learning. Over the past decade, it attracted significant research effort and has been solved for a variety of divergence…
In this paper, we study a notion of local stationarity for discrete time Markov chains which is useful for applications in statistics. In the spirit of some locally stationary processes introduced in the literature, we consider triangular…
An explicit first-order drift-randomized Milstein scheme for a regime switching stochastic differential equation is proposed and its bi-stability and rate of strong convergence are investigated for a non-differentiable drift coefficient.…
We derive some key extremal features for $k$th order Markov chains that can be used to understand how the process moves between an extreme state and the body of the process. The chains are studied given that there is an exceedance of a…