Related papers: A note on the jump locations of Markov processes
We construct a new Markov chain Monte Carlo method on finite states with optimal choices of acceptance-rejection ratio functions. We prove that the constructed continuous time Markov jumping process has a global in-time convergence rate in…
Markov chain Monte Carlo methods explicitly defined on the manifold of probability distributions have recently been established. These methods are constructed from diffusions across the manifold and the solution of the equations describing…
For Markov jump processes on irreducible networks with finite number of sites, we derive a general and explicit expression of the squared coefficient of variation for the net number of transitions from one site to a connected site in a…
We review some developments concerning Markov and Feller processes with jumps in geometric settings. These include stochastic differential equations in Markus canonical form, the Courr\`{e}ge theorem on Lie groups, and invariant Markov…
This paper is devoted to studying the average optimality in continuous-time Markov decision processes with fairly general state and action spaces. The criterion to be maximized is expected average rewards. The transition rates of underlying…
The Semi-Markov property of Continuous Time Random Walks (CTRWs) and their limit processes is utilized, and the probability distributions of the bivariate Markov process $(X(t),V(t))$ are calculated: $X(t)$ is a CTRW limit and $V(t)$ a…
This paper presents a novel theoretical Monte Carlo Markov chain procedure in the framework of graphs. It specifically deals with the construction of a Markov chain whose empirical distribution converges to a given reference one. The Markov…
Recently, a class of stochastic processes known as piecewise deterministic Markov processes has been used to define continuous-time Markov chain Monte Carlo algorithms with a number of attractive properties, including compatibility with…
This paper offers a personal review of some things we've learned about rates of convergence of Markov chains to their stationary distributions. The main topic is ways of speeding up diffusive behavior. It also points to open problems and…
In this paper a method based on a Markov chain Monte Carlo (MCMC) algorithm is proposed to compute the probability of a rare event. The conditional distribution of the underlying process given that the rare event occurs has the probability…
We consider the down/up crossing property of weighted Markov branching processes. The joint probability distribution of multi crossing numbers of such processes are obtained. In particular, for Markov branching processes, the probability…
The asymptotic behavior of the quantum walk on the line is investigated focusing on the probability distribution of chirality independently of position. The long-time limit of this distribution is shown to exist and to depend on the initial…
We study the long-time behavior of variants of the telegraph process with position-dependent jump-rates, which result in a monotone gradient-like drift toward the origin. We compute their invariant laws and obtain, via probabilistic…
We extend the Longstaff-Schwartz algorithm for approximately solving optimal stopping problems on high-dimensional state spaces. We reformulate the optimal stopping problem for Markov processes in discrete time as a generalized statistical…
In this paper, we reveal the branching structure for a non-homogeneous random walk with bounded jumps. The ladder time $T_1,$ the first hitting time of $[1,\infty)$ by the walk starting from $0,$ could be expressed in terms of a…
There has been substantial interest in developing Markov chain Monte Carlo algorithms based on piecewise-deterministic Markov processes. However existing algorithms can only be used if the target distribution of interest is differentiable…
Modern methods of simulating molecular systems are based on the mathematical theory of Markov operators with a focus on autonomous equilibrated systems. However, non-autonomous physical systems or non-autonomous simulation processes are…
Flowgraph models provide an alternative approach in modeling a multi-state stochastic process. One of the most widely used stochastic processes that have many real-world applications especially in actuarial models is the Markov jump process…
In this article, we obtain properties of the law associated to the first hitting time of a threshold by a one-dimensional uniformly elliptic diffusion process and to the associated process stopped at the threshold. Our methodology relies on…
The upper extremes of a Markov chain with regulary varying stationary marginal distribution are known to exhibit under general conditions a multiplicative random walk structure called the tail chain. More generally, if the Markov chain is…