Related papers: Statistical inference for ergodic diffusion with M…
In this paper, we give a sufficient condition for the existence of a quasi-ergodic distribution for absorbing Markov processes. Using an orthogonal-polynomial approach, we prove that the previous main result is valid for the birth-death…
Penalized estimation methods for diffusion processes and dependent data have recently gained significant attention due to their effectiveness in handling high-dimensional stochastic systems. In this work, we introduce an adaptive…
We develop exact Markov chain Monte Carlo methods for discretely-sampled, directly and indirectly observed diffusions. The qualification "exact" refers to the fact that the invariant and limiting distribution of the Markov chains is the…
This paper is devoted to the study of a stochastic process obtained by random switching between a finite collection of vector fields. Such processes have recently been the focus of much attention in the case where the switching times are…
We study ergodic properties of some Markov chains models in random environments when the random Markov kernels that define the dynamic satisfy some usual drift and small set conditions but with random coefficients. In particular, we adapt a…
We consider the problem of the Bayesian inference of drift and diffusion coefficient functions in a stochastic differential equation given discrete observations of a realisation of its solution. We give conditions for the well-posedness and…
In the context of nonparametric Bayesian estimation a Markov chain Monte Carlo algorithm is devised and implemented to sample from the posterior distribution of the drift function of a continuously or discretely observed one-dimensional…
The aim of this article is to prove that diffusion processes in $\mathbb{R}^d$ with a drift can be approximated by suitable Markov chains on $n^{-1}\mathbb{Z}^d$. Moreover, we investigate sufficient conditions on the conductances which…
The aim of this paper is to introduce a new type of test statistic for simple null hypothesis on one-dimensional ergodic diffusion processes sampled at discrete times. We deal with a quasi-likelihood approach for stochastic differential…
We consider the parameter estimation of Markov chain when the unknown transition matrix belongs to an exponential family of transition matrices. Then, we show that the sample mean of the generator of the exponential family is an…
We prove the asymptotic normality of the discretized maximum likelihood estimator for the drift parameter in the homogeneous ergodic diffusion model.
This work develops asymptotic properties of a class of switching jump diffusion processes. The processes under consideration may be viewed as a number of jump diffusion processes modulated by a random switching mechanism. The underlying…
The paper is devoted to studies of perturbed Markov chains commonly used for description of information networks. In such models, the matrix of transition probabilities for the corresponding Markov chain is usually regularised by adding a…
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…
The Markov chain approximation of a one-dimensional symmetric diffusion is investigated in this paper. Given an irreducible reflecting diffusion on a closed interval with scale function $s$ and speed measure $m$, the approximating Markov…
In this paper, we address a model selection problem for ergodic jump diffusion processes based on high-frequency samples. We evaluate the expected genuine log-likelihood function and derive an Akaike-type information criterion based on the…
The concepts of probability, statistics and stochastic theory are being successfully used in structural engineering. Markov Chain modelling is a simple stochastic process model that has found its application in both describing stochastic…
This paper considers estimating the parameters in a regime-switching stochastic differential equation(SDE) driven by Normal Inverse Gaussian(NIG) noise. The model under consideration incorporates a continuous-time finite state Markov chain…
We consider the problem of approximating the stationary distribution of an ergodic Markov chain given a set of sampled transitions. Classical simulation-based approaches assume access to the underlying process so that trajectories of…
Markov chains can be used to generate samples whose distribution approximates a given target distribution. The quality of the samples of such Markov chains can be measured by the discrepancy between the empirical distribution of the samples…