Related papers: One-sided Markov additive processes with lattice a…
Markov chain Monte Carlo methods have become standard tools in statistics to sample from complex probability measures. Many available techniques rely on discrete-time reversible Markov chains whose transition kernels build up over the…
We consider Markov-switching regression models, i.e. models for time series regression analyses where the functional relationship between covariates and response is subject to regime switching controlled by an unobservable Markov chain.…
A scalar Langevin-type process $X(t)$ that is driven by Ornstein-Uhlenbeck noise $\eta(t)$ is non-Markovian. However, the joint dynamics of $X$ and $\eta$ is described by a Markov process in two dimensions. But even though there exists a…
Markov jump processes (or continuous-time Markov chains) are a simple and important class of continuous-time dynamical systems. In this paper, we tackle the problem of simulating from the posterior distribution over paths in these models,…
We present a method to sample Markov-chain trajectories constrained to both the initial and final conditions, which we term Markov bridges. The trajectories are conditioned to end in a specific state at a given time. We derive the master…
Continuous-time Markov chains are mathematical models that are used to describe the state-evolution of dynamical systems under stochastic uncertainty, and have found widespread applications in various fields. In order to make these models…
This work derives a theoretical value for the entropy of a Linear Additive Markov Process (LAMP), an expressive model able to generate sequences with a given autocorrelation structure. While a first-order Markov Chain model generates new…
Particle MCMC involves using a particle filter within an MCMC algorithm. For inference of a model which involves an unobserved stochastic process, the standard implementation uses the particle filter to propose new values for the stochastic…
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…
This paper is a survey of various proofs of the so called {\em fundamental theorem of Markov chains}: every ergodic Markov chain has a unique positive stationary distribution and the chain attains this distribution in the limit independent…
Piecewise-deterministic Markov processes form a general class of non-diffusion stochastic models that involve both deterministic trajectories and random jumps at random times. In this paper, we state a new characterization of the jump rate…
The paper is devoted to the study of lattice paths that consist of vertical steps $(0,-1)$ and non-vertical steps $(1,k)$ for some $k\in \mathbb Z$. Two special families of primary and free lattice paths with vertical steps are considered.…
Recently developed analytic methods in the framework of the Field Correlator Method are reviewed in this series of four lectures and results of calculations are compared to lattice data and experiment. Recent lattice data demonstrating the…
In this paper we present an algorithm for pricing barrier options in one-dimensional Markov models. The approach rests on the construction of an approximating continuous-time Markov chain that closely follows the dynamics of the given…
Multiplex networks (a system of multiple networks that have different types of links but share a common set of nodes) arise naturally in a wide spectrum of fields. Theoretical studies show that in such multiplex networks, correlated edge…
We introduce a family of Markov growth processes on discrete height functions defined on the 2-dimensional square lattice. Each height function corresponds to a configuration of the six vertex model on the infinite square lattice. We focus…
This paper introduces the multiplicative variant of the recently proposed asynchronous additive coarse-space correction method. Definition of an asynchronous extension of multiplicative correction is not straightforward, however, our…
Exclusive diffusion on a one-dimensional lattice is studied. In the model particles hop stochastically into both directions with different rates. At the ends of the lattice particles are injected and removed. The exact stationary…
Fluid approximations have seen great success in approximating the macro-scale behaviour of Markov systems with a large number of discrete states. However, these methods rely on the continuous-time Markov chain (CTMC) having a particular…
In this paper, we are concerned with centered Markov Additive Processes $\{(X_t,Y_t)\}_{t\in\T}$ where the driving Markov process $\{X_t\}_{t\in\T}$ has a finite state space. Under suitable conditions, we provide a local limit theorem for…