Related papers: Analysis of Markov Jump Processes under Terminal C…

In this paper we consider large state space continuous time Markov chains (MCs) arising in the field of systems biology. For density dependent families of MCs that represent the interaction of large groups of identical objects, Kurtz has…

In this paper, we consider an importance sampling problem for a certain rare-event simulations involving the behavior of a diffusion process pertaining to a chain of distributed systems with random perturbations. We also assume that the…

In this paper we develop a perturbation method to predict the rate of occurrence of rare events for singularly perturbed stochastic systems using a probability density function approach. In contrast to a stochastic normal form approach, we…

New results on conditional joint probability distributions of first exit times are presented for a continuous-time stochastic process defined as the mixture of Markov jump processes moving at different speeds on the same finite state space,…

A rescaled Markov chain converges uniformly in probability to the solution of an ordinary differential equation, under carefully specified assumptions. The presentation is much simpler than those in the outside literature. The result may be…

The utilization of model checking has been suggested as a formal verification technique for analyzing critical systems. However, the primary challenge in applying to complex systems is state space explosion problem. To address this issue,…

Here we develop an effective approach to simplify two-time-scale Markov chains with infinite state spaces by removal of states with fast leaving rates, which improves the simplification method of finite Markov chains. We introduce the…

The estimation of absorption time distributions of Markov jump processes is an important task in various branches of statistics and applied probability. While the time-homogeneous case is classic, the time-inhomogeneous case has recently…

Bayesian analysis for Markov jump processes is a non-trivial and challenging problem. Although exact inference is theoretically possible, it is computationally demanding thus its applicability is limited to a small class of problems. In…

It is well-known that 0 is the absorbing state for a branching system. Each particle in the system lives a random long time and gives a random number of new particles at its death time. It stops when the system has no particle. This paper…

Stochastic kinetic models (SKMs) are increasingly used to account for the inherent stochasticity exhibited by interacting populations of species in areas such as epidemiology, population ecology and systems biology. Species numbers are…

The objective of this paper is to study the filtering problem for a system of partially observable processes $(X, Y)$, where $X$ is a non-Markovian pure-jump process representing the signal and $Y$ is a general jump-diffusion which provides…

The challenging problem of conducting fully Bayesian inference for the reaction rate constants governing stochastic kinetic models (SKMs) is considered. Given the challenges underlying this problem, the Markov jump process representation is…

We consider the stochastic ranking process with space-time dependent unbounded jump rates for the particles. We prove that the joint empirical distribution of jump rate and scaled position converges almost surely to a deterministic…

The aim of this paper is to approximate a finite-state Markov process by another process with fewer states, called herein the approximating process. The approximation problem is formulated using two different methods. The first method,…

In this article, we consider a receding horizon control of discrete-time state-dependent jump linear systems, particular kind of stochastic switching systems, subject to possibly unbounded random disturbances and probabilistic state…

A common problem that affects simulations of complex systems within the computational physics and chemistry communities is the so-called sampling problem or rare event problem where proper sampling of energy landscapes is impeded by the…

In this paper, we propose a class of efficient, accurate, and general methods for solving state-estimation problems with equality and inequality constraints. The methods are based on recent developments in variable splitting and partially…

We consider chance-constrained problems with discrete random distribution. We aim for problems with a large number of scenarios. We propose a novel method based on the stochastic gradient descent method which performs updates of the…

State-of-the-art methods for rare event simulation of non-Markovian models face practical or theoretical limits if observing the event of interest requires prior knowledge or information on the timed behavior of the system. In this paper,…