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Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input…

This paper presents a numerical method to calculate the value function for a general discounted impulse control problem for piecewise deterministic Markov processes. Our approach is based on a quantization technique for the underlying…

Motivated by entropic optimal transport, time reversal of Markov jump processes in $\mathbb{R}^n$ is investigated. Relying on an abstract integration by parts formula for the carr\'e du champ of a Markov process recently obtained by…

The Reversible Jump algorithm is one of the most widely used Markov chain Monte Carlo algorithms for Bayesian estimation and model selection. A generalized multiple-try version of this algorithm is proposed. The algorithm is based on…

We study the error of reversible Markov chain Monte Carlo methods for approximating the expectation of a function. Explicit error bounds with respect to different norms of the function are proven. By the estimation the well known…

An important task in machine learning and statistics is the approximation of a probability measure by an empirical measure supported on a discrete point set. Stein Points are a class of algorithms for this task, which proceed by…

A novel class of non-reversible Markov chain Monte Carlo schemes relying on continuous-time piecewise-deterministic Markov Processes has recently emerged. In these algorithms, the state of the Markov process evolves according to a…

The Markov Chain Monte Carlo method is the dominant paradigm for posterior computation in Bayesian analysis. It is common to control computation time by making approximations to the Markov transition kernel. Comparatively little attention…

A possibly time-dependent transition intensity matrix or generator $(Q(t))$ characterizes the law of a Markov jump process (MP). For a time homogeneous MP, the transition probability matrix (TPM) can be expressed as a matrix exponential of…

Markov automata combine non-determinism, probabilistic branching, and exponentially distributed delays. This compositional variant of continuous-time Markov decision processes is used in reliability engineering, performance evaluation and…

We investigate the concatenation of Markov processes. Our primary concern is to utilize processes constructed in this manner for Monte Carlo integration. To enable this using conventional methods, it is essential to demonstrate the Markov…

Markov chain Monte Carlo (MCMC) algorithms are indispensable when sampling from a complex, high-dimensional distribution by a conventional method is intractable. Even though MCMC is a powerful tool, it is also hard to control and tune in…

Large deviations for additive path functionals of stochastic processes have attracted significant research interest, in particular in the context of stochastic particle systems and statistical physics. Efficient numerical `cloning'…

We establish a new Bernstein-type deviation inequality for general (non-reversible) discrete-time Markov chains via an elementary approach. More robust than existing works in the literature, our result only requires the Markov chain to…

Verification of infinite-state Markov chains is still a challenge despite several fruitful numerical or statistical approaches. For decisive Markov chains, there is a simple numerical algorithm that frames the reachability probability as…

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…

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…

Markov chain Monte Carlo (MCMC) is a powerful tool for sampling from complex probability distributions. Despite its versatility, MCMC often suffers from strong autocorrelation and the negative sign problem, leading to slowing down the…

We define the probability structure of a continuous-time time-homogeneous Markov jump process, on a finite graph, that represents the continuous-time counterpart of the so-called Ruelle-Bowen discrete-time random walk. It constitutes the…

For continuous-time Markov jump processes on irreducible networks with time-independent rate constants, we employ a transition-based formalism to express the long-time precision of a single integrated current over an observable channel in…