相关论文: Extending Chacon-Walsh: minimality and generalised…
This paper develops mixed-normal approximations for probabilities that vectors of multiple Skorohod integrals belong to random convex polytopes when the dimensions of the vectors possibly diverge to infinity. We apply the developed theory…
Given a L\'evy process $L$, we consider the so-called statistical Skorohod embedding problem of recovering the distribution of an independent random time $T$ based on i.i.d. sample from $L_{T}.$ Our approach is based on the genuine use of…
This paper studies limit theorems for Markov Chains with general state space under conditions which imply subgeometric ergodicity. We obtain a central limit theorem and moderate deviation principles for additive not necessarily bounded…
Fedorchuk's fully closed (continuous) maps and resolutions are applied in constructions of non-metrizable higher-dimensional analogues of Anderson, Choquet, and Cook's continua. Certain theorems on dimension-lowering maps are proved for…
We develop a class of pathwise inequalities of the form $H(B_t)\ge M_t+F(L_t)$, where $B_t$ is Brownian motion, $L_t$ its local time at zero and $M_t$ a local martingale. The concrete nature of the representation makes the inequality useful…
We consider cost minimizing stopping time solutions to Skorokhod embedding problems, which deal with transporting a source probability measure to a given target measure through a stopped Brownian process. PDEs and a free boundary problem…
In this paper, one considers the coupling of a Brinkman model and Stokes equations with jump embedded transmission conditions. In this model, one assumes that the viscosity in the porous region is very small. Then we derive a…
In this paper, we provide an alternative proof of the monotonicity principle for the optimal Skorokhod embedding problem established by Beiglb\"ock, Cox and Huesmann. This principle presents a geometric characterization that reflects the…
Motivated by global warming issues, we consider a time se- ries that consists of a nondecreasing trend observed with station- ary fluctuations, nonparametric estimation of the trend under monotonicity assumption is considered. The rescaled…
We consider the problem of sampling a multimodal distribution with a Markov chain given a small number of samples from the stationary measure. Although mixing can be arbitrarily slow, we show that if the Markov chain has a $k$th order…
In this work, we investigate the problem of the boundedness of the Gross' solutions of the planar Skorokhod embedding problem, where we show that the solution is bounded under some mild conditions on the underlying probability distribution.
The present paper focuses on the problem of sampling from a given target distribution $\pi$ defined on some general state space. To this end, we introduce a novel class of non-reversible Markov chains, each chain being defined on an…
We establish conditions under which a continuous time reservoir computer, such as a leaky integrator echo state network, admits a generalised synchronisation $f$ between between the source dynamics and reservoir dynamics. We show that…
This paper links at the formal level the entropy structure of a multi-species cross-diffusion system of Shigesada-Kawasaki-Teramoto (SKT) type satisfying the detailed balance condition with the entropy structure of a reversible microscopic…
A divide-and-conquer approach to analyzing Markov chains (MCs) is not utilized as widely as it could be, despite its potential benefits. One primary reason for this is the fact that most MC decomposition approaches involve a complex and…
Recently Johansson and Rahman obtained the limiting multi-time distribution for the discrete polynuclear growth model, which is equivalent to a discrete TASEP model with step initial condition. In this paper, we obtain a finite time…
We study higher order expansions both in the Berry-Ess\'een estimate (Edgeworth expansions) and in the local limit theorems for Birkhoff sums of chaotic probability preserving dynamical systems. We establish general results under technical…
We introduce the Markov extension, represented schematically as a tower, to the study of dynamical systems with holes. For tower maps with small holes, we prove the existence of conditionally invariant probability measures which are…
The Cauchy problem is studied for very general systems of evolution equations, where the time derivative of solution is written by Fourier multipliers in space and analytic nonlinearity, with no other structural requirement. We construct a…
In [1] a detailed analysis was given of the large-time asymptotics of the total mass of the solution to the parabolic Anderson model on a supercritical Galton-Watson random tree with an i.i.d. random potential whose marginal distribution is…