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We develop a semi-parametric state-space model for time-series data with latent regime transitions. Classical Markov-switching models use fixed parametric transition functions, such as logistic or probit links, which restrict flexibility…

Markov chains are fundamental models for stochastic dynamics, with applications in a wide range of areas such as population dynamics, queueing systems, reinforcement learning, and Monte Carlo methods. Estimating the transition matrix and…

This work proposes a general framework for capturing noise-driven transitions in spatially extended non-equilibrium systems and explains the emergence of coherent patterns beyond the instability onset. The framework relies on stochastic…

Multistate Markov models are a canonical parametric approach for data modeling of observed or latent stochastic processes supported on a finite state space. Continuous-time Markov processes describe data that are observed irregularly over…

Regime-switching models, in particular Hidden Markov Models (HMMs) where the switching is driven by an unobservable Markov chain, are widely-used in financial applications, due to their tractability and good econometric properties. In this…

Forecasting based on financial time-series is a challenging task since most real-world data exhibits nonstationary property and nonlinear dependencies. In addition, different data modalities often embed different nonlinear relationships…

We investigate nonlinear regression for nonstationary sequential data. In most real-life applications such as business domains including finance, retail, energy and economy, timeseries data exhibits nonstationarity due to the temporally…

Continuous-time Markov chains are used to model stochastic systems where transitions can occur at irregular times, e.g., birth-death processes, chemical reaction networks, population dynamics, and gene regulatory networks. We develop a…

We propose a novel method to directly learn a stochastic transition operator whose repeated application provides generated samples. Traditional undirected graphical models approach this problem indirectly by learning a Markov chain model…

Markov switching models are a popular family of models that introduces time-variation in the parameters in the form of their state- or regime-specific values. Importantly, this time-variation is governed by a discrete-valued latent…

Misperceptions about extreme dependencies between different financial assets have been an im- portant element of the recent financial crisis. This paper studies inhomogeneity in dependence structures using Markov switching regular vine…

Time series and signals are attracting more attention across statistics, machine learning and pattern recognition as it appears widely in the industry especially in sensor and IoT related research and applications, but few advances has been…

Markov branching systems form a fundamental class of stochastic models that are extensively applied in biology, physics, finance, and other domains. These systems are distinguished by their continuous-time evolution and inherent branching…

We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to…

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…

A mathematical framework for Continuous Time Finance based on operator algebraic methods offers a new direct and entirely constructive perspective on the field and leads to new numerical analysis techniques. This is partly a review paper as…

The rigorous linking of exact stochastic models to mean-field approximations is studied. Starting from the differential equation point of view the stochastic model is identified by its Kolmogorov equations, which is a system of linear ODEs…

The classical embeddability problem asks whether a given stochastic matrix $T$, describing transition probabilities of a $d$-level system, can arise from the underlying homogeneous continuous-time Markov process. Here, we investigate the…

In this paper, we propose a data-driven robust safety verification framework for stochastic dynamical systems modeled as Markov decision processes with time-varying and uncertain transition probabilities. Rather than assuming access to the…

This script offers an implementation-oriented introduction to deep learning methods for solving and estimating high-dimensional dynamic stochastic models in economics and finance. Its starting point is the curse of dimensionality:…