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Normalizing flows, diffusion normalizing flows and variational autoencoders are powerful generative models. This chapter provides a unified framework to handle these approaches via Markov chains. We consider stochastic normalizing flows as…

The main contribution of this paper is to present a new sufficient condition for the subexponential asymptotics of the stationary distribution of a GI/GI/1-type Markov chain without jumps from level "infinity" to level zero. For simplicity,…

Key challenges in the analysis of highly multivariate large-scale spatial stochastic processes, where both the number of components (p) and spatial locations (n) can be large, include achieving maximal sparsity in the joint precision…

In this paper we consider the problem of computing the stationary distribution of nearly completely decomposable Markov processes, a well-established area in the classical theory of Markov processes with broad applications in the design,…

Stochastic reaction networks (SRNs) model stochastic effects for various applications, including intracellular chemical or biological processes and epidemiology. A typical challenge in practical problems modeled by SRNs is that only a few…

While single-purchase choice models have been widely studied in assortment optimization, customers in modern retail and e-commerce environments often purchase multiple items across distinct product categories, exhibiting both substitution…

This chapter presents an introduction to Markovian modeling for the analysis of sequence data. Contrary to the deterministic approach seen in the previous sequence analysis chapters, Markovian models are probabilistic models, focusing on…

The single server queue with multiple customer types and semi-Markovian service times, sometimes referred to as the $M/SM/1$ queue, has been well-studied since its introduction by Neuts in 1966. In this paper, we apply an extension of this…

We propose a flexible stochastic framework for modeling the market share dynamics over time in a multiple markets setting, where firms interact within and between markets. Firms undergo stochastic idiosyncratic shocks, which contract their…

This paper proposes a hierarchical modeling approach to perform stochastic model specification in Markov switching vector error correction models. We assume that a common distribution gives rise to the regime-specific regression…

Supermarket models are a class of interesting parallel queueing networks with dynamic randomized load balancing and real-time resource management. When the parallel servers are subject to breakdowns and repairs, analysis of such a…

Traditional methods for unsupervised learning of finite mixture models require to evaluate the likelihood of all components of the mixture. This becomes computationally prohibitive when the number of components is large, as it is, for…

Markov-modulated fluid queues are popular stochastic processes frequently used for modelling real-life applications. An important performance measure to evaluate in these applications is their steady-state behaviour, which is determined by…

Phase type (PH) distributions are widely used in modeling and simulation due to their generality and analytical properties. In such settings, it is often necessary to construct a PH distribution that aligns with real-world data by matching…

We introduce an extension of finite mixture models by incorporating skew-normal distributions within a Hidden Markov Model framework. By assuming a constant transition probability matrix and allowing emission distributions to vary according…

We develop theoretical equivalences between stochastic and deterministic models for populations of individual cells stratified by age. Specifically, we develop a hierarchical system of equations describing the full dynamics of an…

We propose a Bayesian nonparametric mixture model for prediction- and information extraction tasks with an efficient inference scheme. It models categorical-valued time series that exhibit dynamics from multiple underlying patterns (e.g.…

Understanding the fluctuations by which phenomenological evolution equations with thermodynamic structure can be enhanced is the key to a general framework of nonequilibrium statistical mechanics. These fluctuations provide an idealized…

Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…

Many biological and medical questions can be modeled using time-to-event data in finite-state Markov chains, with the phase-type distribution describing intervals between events. We solve the inverse problem: given a phase-type…