Related papers: Conditioning continuous-time Markov processes by g…

Experiments, in particular on biological systems, typically probe lower-dimensional observables which are projections of high-dimensional dynamics. In order to infer consistent models capturing the relevant dynamics of the system, it is…

We consider the task of filtering a dynamic parameter evolving as a diffusion process, given data collected at discrete times from a likelihood which is conjugate to the marginal law of the diffusion, when a generic dual process on a…

This paper is concerned with the development of rigorous approximations to various expectations associated with Markov chains and processes having non-stationary transition probabilities. Such non-stationary models arise naturally in…

For a continuous-time Markov process, we characterize the law of the first jump location when started from an arbitrary initial distribution, in terms of the invariant distribution of an auxiliary Markov process. This could be of interest…

We describe an exact approach for calculating transition probabilities and waiting times in finite-state discrete-time Markov processes. All the states and the rules for transitions between them must be known in advance. We can then…

We study the evolution of a particle system whose genealogy is given by a supercritical continuous time Galton--Watson tree. The particles move independently according to a Markov process and when a branching event occurs, the offspring…

Reinforced processes are known to provide a stochastic representation for the quasi-stationary distribution of a given killed Markov process - describing the killed Markov process at fixed time instants. In this paper we shall adapt the…

We are studying stationary random processes with conditional polynomial moments that allow a continuous path modification. Processes with continuous path modification, are important because they are relatively easy to simulate. One does not…

Studying the behaviour of Markov processes at boundary points of the state space has a long history, dating back all the way to William Feller. With different motivations in mind entrance and exit questions have been explored for different…

Lumping a Markov process introduces a coarser level of description that is useful in many contexts and applications. The dynamics on the coarse grained states is often approximated by its Markovian component. In this letter we derive…

For controlled discrete-time stochastic processes we introduce a new class of dynamic risk measures, which we call process-based. Their main features are that they measure risk of processes that are functions of the history of a base…

We study the long time behaviour of a Markov process evolving in $\mathbb{N}$ and conditioned not to hit 0. Assuming that the process comes back quickly from infinity, we prove that the process admits a unique quasi-stationary distribution…

Focusing on stochastic systems arising in mean-field models, the systems under consideration belong to the class of switching diffusions, in which continuous dynamics and discrete events coexist and interact. The discrete events are modeled…

In this paper, we proved moderate deviation principles for a fully coupled two-time-scale stochastic systems, where the slow process is given by stochastic differential equations with small noise, while the fast process is a rapidly…

Consider an N-dimensional Markov chain obtained from N one-dimensional random walks by Doob h-transform with the q-Vandermonde determinant. We prove that as N becomes large, these Markov chains converge to an infinite-dimensional Feller…

Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…

We provide a coupling proof of Doob's theorem which says that the transition probabilities of a regular Markov process which has an invariant probability measure $\mu$ converge to $\mu$ in the total variation distance. In addition we show…

We introduce a statistical mechanics formalism for the study of constrained graph evolution as a Markovian stochastic process, in analogy with that available for spin systems, deriving its basic properties and highlighting the role of the…

This paper aims to establish a central limit theorem for Markov processes conditioned not to be absorbed under a very general assumption on quasi-stationarity for the underlying process. To do so, a central limit theorem has been…

In this paper we propose a new method for approximating the nonstationary moment dynamics of one dimensional Markovian birth-death processes. By expanding the transition probabilities of the Markov process in terms of Poisson-Charlier…