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We study two models of Anderson-type random operators on two deterministically coupled continuous strings. Each model is associated with independent, identically distributed four-by-four symplectic transfer matrices, which describe the…

We consider continuous-time Markov chains on integers which allow transitions to adjacent states only, with alternating rates. We give explicit formulas for probability generating functions, and also for means, variances and state…

The aim of this note is to give a straightforward proof of a general version of the Ciesielski-Taylor identity for positive self-similar Markov processes of the spectrally negative type which umbrellas all previously known Ciesielski-Taylor…

The switch process alternates independently between 1 and -1, with the first switch to 1 occurring at the origin. The expected value function of this process is defined uniquely by the distribution of switching times. The relation between…

Due to \v{C}encov's theorem, there exists a unique family of invariant symmetric $(0,2)$-tensor fields on the space of positive probability measures on a set of $n$-points indexed by $n\in \mathbb{N}$ under Markov embeddings. We deform…

Stochastic convergence of discrete time Markov processes has been analysed based on a dual Lyapunov approach. Using some existing results on ergodic theory of Markov processes, it has been shown that existence of a properly subinvariant…

We study a unitary version of the one-dimensional Anderson model, given by a five diagonal deterministic unitary operator multiplicatively perturbed by a random phase matrix. We fully characterize positivity and vanishing of the Lyapunov…

Piecewise Deterministic Monte Carlo algorithms enable simulation from a posterior distribution, whilst only needing to access a sub-sample of data at each iteration. We show how they can be implemented in settings where the parameters live…

We investigate a piecewise-deterministic Markov process, evolving on a Polish metric space, whose deterministic behaviour between random jumps is governed by some semi-flow, and any state right after the jump is attained by a randomly…

This study in centered on models accounting for stochastic deformations of sample paths of random walks, embedded either in $\mathbb{Z}^2$ or in $\mathbb{Z}^3$. These models are immersed in multi-type particle systems with exclusion.…

The paper deals with a certain class of random evolutions. We develop a construction that yields an invariant measure for a continuous-time Markov process with random transitions. The approach is based on a particular way of constructing…

We consider a certain sequence of random walks. The state space of the n-th random walk is the set of all strict partitions of n (that is, partitions without equal parts). We prove that, as n goes to infinity, these random walks converge to…

We consider statistical Markov Decision Processes where the decision maker is risk averse against model ambiguity. The latter is given by an unknown parameter which influences the transition law and the cost functions. Risk aversion is…

We introduce a new random graph model motivated by biological questions relating to speciation. This random graph is defined as the stationary distribution of a Markov chain on the space of graphs on $\{1, \ldots, n\}$. The dynamics of this…

Discriminative latent variable models (LVM) are frequently applied to various visual recognition tasks. In these systems the latent (hidden) variables provide a formalism for modeling structured variation of visual features. Conventionally,…

For general penalized Markov processes with soft killing, we propose a simple criterion ensuring uniform convergence of conditional distributions in Wasserstein distance to a unique quasi-stationary distribution. We give several examples of…

Random Bridges have gained significant attention in recent years due to their potential applications in various areas, particularly in information-based asset pricing models. This paper aims to explore the potential influence of the pinning…

For a broad class of point processes, including determinantal point processes, we construct associated marked and conditional ensembles, which allow to study a random configuration in the point process, based on information about a randomly…

We prove a conjecture of Diaconis and Freedman (Ann. Probab. 1980) characterising the extreme points of the set of partially-exchangeable processes on a countable set. More concretely, we prove that the partially exchangeable sigma-algebra…

We are studying stationary random processes with conditional polynomial moments that allow a continuous path modification. Processes with continuous path modification, are important because they are relatively easy to simulate. One does not…