Piecewise deterministic Markov processes are an important new tool in the design of Markov
Chain Monte Carlo algorithms. Two examples of fundamental importance are the Bouncy …

The use of higher-order stochastic processes such as nonlinear Markov chains or vertex-
reinforced random walks is significantly growing in recent years as they are much better at …

Piecewise deterministic Markov processes are an important new tool in the design of Markov
chain Monte Carlo algorithms. Two examples of fundamental importance are the bouncy …

Abstract Recently, in [11], the “coin-turning walk” was introduced on Z. It is a non-Markovian
process where the steps form a (possibly) time-inhomogeneous Markov chain. In this article …

Let S be the random walk obtained from “coin turning” with some sequence {p_n\}_n≥2, as
introduced in 8. In this paper we investigate the scaling limits of S in the spirit of the classical …

We connect the empirical or 'occupation'laws of certain discrete space time-inhomogeneous
Markov chains, related to simulated annealing, to a novel class of 'stick-breaking'processes …

In a general stochastic multistate promoter model of dynamic messenger ribonucleic acid
(mRNA)/protein interactions, we identify the stationary joint distribution of the promoter state …

The chapter is based on [17] with János Engländer and Stanislav Volkov, in which we study
the scaling limit of the coin-turning walk. This random walk describes the sum of sequence of …

We study the connections among three types of objects: Residual Allocation Models (RAMs),
a generalized class of stick-breaking processes which include Dirichlet processes, and the …