Related papers: A multi-dimensional Markov chain and the Meixner e…
First-passage times are often the most relevant aspect of a complex Markovian network, because they signify when information processing has resulted in a definite decision. Previous studies have shown that for kinetic proofreading networks…
The switch chain is a well-known Markov chain for sampling directed graphs with a given degree sequence. While not ergodic in general, we show that it is ergodic for regular degree sequences. We then prove that the switch chain is rapidly…
We calculate crossing probabilities and one-sided last exit time densities for a class of moving barriers on an interval $[0,T]$ via Schwartz distributions. We derive crossing probabilities and first hitting time densities for another class…
Given a permutation sigma of the integers {-n,-n+1,...,n} we consider the Markov chain X_{sigma}, which jumps from k to sigma (k\pm 1) equally likely if k\neq -n,n. We prove that the expected hitting time of {-n,n} starting from any point…
Markov chain Monte Carlo methods explicitly defined on the manifold of probability distributions have recently been established. These methods are constructed from diffusions across the manifold and the solution of the equations describing…
We give sharp two-sided estimates for the functions $g_M(t,x,y)$ and $g_M(t,x,y)-g(t,x,y)$, where $g_M(t,x,y)$ are the transition probability densities of the reflected Brownian motion on a $M$-complex of size $M \in \mathbb{Z}$ of an…
A sequence of real numbers (x_n) is Benford if the significands, i.e. the fraction parts in the floating-point representation of (x_n) are distributed logarithmically. Similarly, a discrete-time irreducible and aperiodic finite-state Markov…
We present a MATLAB package, which is the first of its kind, for Higher Order Markov Chains (HOMC). It can be used to easily compute all important quantities in our recent works relevant to higher order Markov chains, such as the $k$-step…
We define a finite Markov chain, called generalized crested product, which naturally appears as a generalization of the first crested product of Markov chains. A complete spectral analysis is developed and the $k$-step transition…
We consider a a collection of categorical random variables. Of special interest is the causal effect on an outcome variable following an intervention on another variable. Conditionally on a Directed Acyclic Graph (DAG), we assume that the…
We study the existence of densities for distributions of piecewise deterministic Markov processes. We also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times. In…
It is shown that the polynuclear growth model is a completely integrable Markov process in the sense that its transition probabilities are given by Fredholm determinants of kernels produced by a scattering transform based on the invariant…
In this work we consider time series with a finite number of discrete point changes. We assume that the data in each segment follows a different probability density functions (pdf). We focus on the case where the data in all segments are…
The present paper focuses on the problem of sampling from a given target distribution $\pi$ defined on some general state space. To this end, we introduce a novel class of non-reversible Markov chains, each chain being defined on an…
We analyze the probability distributions of the quantum walks induced from Markov chains by Szegedy (2004). The first part of this paper is devoted to the quantum walks induced from finite state Markov chains. It is shown that the…
We consider triangular arrays of Markov chains that converge weakly to a diffusion process. Edgeworth type expansions of third order for transition densities are proved. This is done for time horizons that converge to 0. For this purpose we…
Perturbation theory for Markov chains addresses the question how small differences in the transitions of Markov chains are reflected in differences between their distributions. We prove powerful and flexible bounds on the distance of the…
This paper introduces a Bayesian framework that combines Markov chain Monte Carlo (MCMC) sampling, dimensionality reduction, and neural density estimation to efficiently handle inverse problems that (i) must be solved multiple times, and…
In this article, the following results are obtained: the process of a randomly wandering particle having a size and a continuous trajectory of motion is considered; (b) based on the study of this probabilistic process, a derivation of the…
This paper presents a study of the properties of a matrix model that was introduced to describe transitions between all Wigner surmises of Random Matrix theory. New results include closed-form exact analytical expressions for the…