Related papers: The exit time finite state projection scheme: boun…
In the analysis of Markov chains and processes, it is sometimes convenient to replace an unbounded state space with a "truncated" bounded state space. When such a replacement is made, one often wants to know whether the equilibrium behavior…
The chemical master equation (CME) is frequently used in systems biology to quantify the effects of stochastic fluctuations that arise due to biomolecular species with low copy numbers. The CME is a system of ordinary differential equations…
We present an adaptive Finite State Projection (FSP) method for efficiently solving the Chemical Master Equation (CME) with rigorous error control. Our approach integrates time-stepping with dynamic state-space truncation, balancing…
The Finite State Projection (FSP) method approximates the Chemical Master Equation (CME) by restricting the dynamics to a finite subset of the (typically infinite) state space, enabling direct numerical solution with computable error…
Computing the stationary distributions of a continuous-time Markov chain (CTMC) involves solving a set of linear equations. In most cases of interest, the number of equations is infinite or too large, and the equations cannot be solved…
The time at which a one-dimensional continuous strong Markov process attains a boundary point of its state space is a discontinuous path functional and it is, therefore, unclear whether the exit time can be approximated by hitting times of…
In the analysis of Markov chains and processes, it is sometimes convenient to replace an unbounded state space with a "truncated" bounded state space. When such a replacement is made, one often wants to know whether the equilibrium behavior…
This work introduces a notion of approximate probabilistic trace equivalence for labelled Markov chains, and relates this new concept to the known notion of approximate probabilistic bisimulation. In particular this work shows that the…
Many probabilistic inference problems such as stochastic filtering or the computation of rare event probabilities require model analysis under initial and terminal constraints. We propose a solution to this bridging problem for the widely…
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,…
We recently proposed a method for estimation of states and parameters in stochastic differential equations, which included intermediate time points between observations and used the Laplace approximation to integrate out these intermediate…
We examine an analytic variational inference scheme for the Gaussian Process State Space Model (GPSSM) - a probabilistic model for system identification and time-series modelling. Our approach performs variational inference over both the…
To understand the long-run behavior of Markov population models, the computation of the stationary distribution is often a crucial part. We propose a truncation-based approximation that employs a state-space lumping scheme, aggregating…
A novel method is presented to compute the exit time for the stochastic simulation algorithm. The method is based on the addition of a series of random variables and is derived using the convolution theorem. The final distribution is…
This paper deals with the problem of remote estimation of the state of a discrete-time stochastic linear system observed by a sensor with computational capacity to calculate local estimates. We design an event-triggered communication (ETC)…
We derive a novel variational expectation maximization approach based on truncated posterior distributions. Truncated distributions are proportional to exact posteriors within subsets of a discrete state space and equal zero otherwise. The…
This paper introduces a new algorithm for numerically computing equilibrium (i.e. stationary) distributions for Markov chains and Markov jump processes with either a very large finite state space or a countably infinite state space. The…
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,…
We consider continuous time Markovian processes where populations of individual agents interact stochastically according to kinetic rules. Despite the increasing prominence of such models in fields ranging from biology to smart cities,…
In this paper we consider approximations to the popular Pitman-Yor process obtained by truncating the stick-breaking representation. The truncation is determined by a random stopping rule that achieves an almost sure control on the…