Related papers: Markov chain approximations for nonsymmetric proce…
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…
Markov chain Monte Carlo methods are central in computational statistics, and typically rely on detailed balance to ensure invariance with respect to a target distribution. Although straightforward to construct by Metropolization, this can…
Fluid approximations have seen great success in approximating the macro-scale behaviour of Markov systems with a large number of discrete states. However, these methods rely on the continuous-time Markov chain (CTMC) having a particular…
We derive consistency and asymptotic normality results for quasi-maximum likelihood methods for drift parameters of ergodic stochastic processes observed in discrete time in an underlying continuous-time setting. The special feature of our…
We give sufficient conditions for Mosco convergences for the following three cases: symmetric locally uniformly elliptic diffusions, symmetric L\'evy processes, and symmetric jump processes in terms of the $L^1(\mathbb R;dx)$-local…
We introduce a model with diffusive and evaporation/condensation processes, depending on 3 parameters obeying some inequalities. The model can be solved in the sense that all correlation functions can be computed exactly without the use of…
The most common way to sample from a probability distribution is to use Monte-Carlo methods. For distributions on a continuous state space, one can find diffusions with the target distribution as equilibrium measure, so that the state of…
We describe stochastic calculus in the context of processes that are driven by an adapted point process of locally finite intensity and are differentiable between jumps. This includes Markov chains as well as non-Markov processes. By…
In the article the distributions of overjump functionals for almost semi-continuous processes on a finite irreducible Markov chain are considered.
Motivated by applications to proving regularity of solutions to degenerate parabolic equations arising in population genetics, we study existence, uniqueness and the strong Markov property of weak solutions to a class of degenerate…
We are interested in the asymptotic behavior of Markov chains on the set of positive integers for which, loosely speaking, large jumps are rare and occur at a rate that behaves like a negative power of the current state, and such that small…
We present new conditions on the drift of the Morrey type with mixed norms allowing us to obtain Aleksandrov type estimates of potentials of time inhomogeneous diffusion processes in spaces with mixed norms and, for instance, in…
We investigate the problem of quantifying contraction coefficients of Markov transition kernels in Kantorovich ($L^1$ Wasserstein) distances. For diffusion processes, relatively precise quantitative bounds on contraction rates have recently…
We study a class of Markov processes with finite state space and continuous time that have product form stationary distributions. We obtain a number of examples that can generate conjectures for diffusions with inert drift.
We develop the first exact Bayesian methodology for the problem of inference in discretely observed regime switching diffusions. Switching diffusion models extend ordinary diffusions by allowing for jumps in instantaneous drift and…
This paper provides convergence analysis for the approximation of a class of path-dependent functionals underlying a continuous stochastic process. In the first part, given a sequence of weak convergent processes, we provide a sufficient…
We prove that for a random walk on the real line whose increments have zero mean and are either integer-valued or spread out (i.e. the distributions of the steps of the walk are eventually non-singular), the Markov chain of overshoots above…
In this paper, we study properties of the dual process and Schrodinger-type operators of a non-symmetric diffusion with measure-valued drift. Let mu=(mu^1,..., mu^d) be such that each mu^i is a signed measure on R^d belonging to the Kato…
We propose a novel, tractable latent state inference scheme for Markov jump processes, for which exact inference is often intractable. Our approach is based on an entropic matching framework that can be embedded into the well-known…
We provide explicit nonasymptotic estimates for the rate of convergence of empirical means of Markov chains, together with a Gaussian or exponential control on the deviations of empirical means. These estimates hold under a "positive…