Related papers: Quasi-continuous random variables and processes un…
We study the existence of densities for distributions of piecewise deterministic Markov processes. We also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times. In…
Quasi-stationary distributions (QSD) have been widely studied since the pioneering work of Kolmogorov (1938), Yaglom (1947) and Sevastyanov (1951). They appear as a natural object when considering Markov processes that are certainly…
We establish Krylov-Safonov type H\"older regularity theory for solutions to quite general discrete dynamic programming equations or equivalently discrete stochastic processes on random geometric graphs. Such graphs arise for example from…
The standard approach to analyzing the asymptotic complexity of probabilistic programs is based on studying the asymptotic growth of certain expected values (such as the expected termination time) for increasing input size. We argue that…
We discuss the concepts of quasi-renewal and quasi-regenerative processes. We also propose a method for obtaining the upper bounds for the convergence rate of the distribution of a regenerative and quasi-regenerative process to a stationary…
We construct flexible likelihoods for multi-output Gaussian process models that leverage neural networks as components. We make use of sparse variational inference methods to enable scalable approximate inference for the resulting class of…
The aim of this paper is to present an elementary computable theory of probability, random variables and stochastic processes. The probability theory is baed on existing approaches using valuations and lower integrals. Various approaches to…
Maximum likelihood estimators for time-dependent mean functions within Gaussian processes are provided in the context of continuous observations. We find the widest possible class of mean functions for which the likelihood function can be…
We seek to infer the parameters of an ergodic Markov process from samples taken independently from the steady state. Our focus is on non-equilibrium processes, where the steady state is not described by the Boltzmann measure, but is…
This note provides several recent progresses in the study of long time behavior of Markov processes. The examples presented below are related to other scientific fields as PDE's, physics or biology. The involved mathematical tools as…
In this paper we prove a discretized version of Krylov's estimate for discretized It\^o's processes. As applications, we study the weak and strong convergences for Euler's approximation of mean-field SDEs with measurable discontinuous and…
We consider the Markov chain approximations for singular stable-like processes. First we obtain properties of some Markov chains. Then we construct the approximating Markov chains and give a necessary condition for weak convergence of these…
Latent variable models are widely used to account for unobserved determinants of economic behavior. This paper introduces a quasi-Bayes approach to nonparametrically estimate a large class of latent variable models. As an application, we…
We consider a semiclassical random walk with respect to a probability measure associated to a potential with a finite number of critical points. We recover the spectral results from [1] on the corresponding operator in a more general…
We present the modified approach to the classical Bogolyubov-Krylov averaging, developed recently for the purpose of PDEs. It allows to treat Lipschitz perturbations of linear systems with pure imaginary spectrum and may be generalized to…
In this paper, a modification of the conventional approximations to the quasi-maximum likelihood method is introduced for the parameter estimation of diffusion processes from discrete observations. This is based on a convergent…
We investigate the frequentist guarantees of the variational sparse Gaussian process regression model. In the theoretical analysis, we focus on the variational approach with spectral features as inducing variables. We derive guarantees and…
We consider the problem of inferring a latent function in a probabilistic model of data. When dependencies of the latent function are specified by a Gaussian process and the data likelihood is complex, efficient computation often involve…
The asymptotic normality in multi-dimension of the nonparametric estimator of the transition probabilities of a Markov renewal chain is proved, and is applied to that of other nonparametric estimators involved with the associated…
It is common, when dealing with quantum processes involving a subsystem of a much larger composite closed system, to treat them as effectively memory-less (Markovian). While open systems theory tells us that non-Markovian processes should…