Related papers: Sensitivity analysis for finite Markov chains in d…
We study inhomogeneous continuous-time weakly ergodic Markov chains with a finite state space. We introduce the notion of a Markov chain with the regular structure of an infinitesimal matrix and study the sharp upper bounds on the rate of…
We are interested in studying the sensitivity of diffusion processes or their approximations by Markov Chains with respect to a perturbation of the coefficients.
We establish convergence to an invariant measure as time tends to infinity, for a large class of (possibly non-Markovian) stochastic volatility models. Our arguments are based on a novel coupling idea for Markov chains which also extends to…
Probabilistic model checking for systems with large or unbounded state space is a challenging computational problem in formal modelling and its applications. Numerical algorithms require an explicit representation of the state space, while…
Response theory provides a pathway for understanding the sensitivity of a system and for predicting how its statistical properties change when a perturbation is applied. In the case of complex and multiscale systems, to achieve enhanced…
The stochastic properties of a Langevin-type Markov process can be extracted from a given time series by a Markov analysis. Also processes that obey a stochastically forced second order differential equation can be analyzed this way by…
We consider the Markov chain approximations for singular stable-like processes. First we obtain properties of some Markov chains. Then we construct the approximating Markov chains and give a necessary condition for weak convergence of these…
Even simply-defined, finite-state generators produce stochastic processes that require tracking an uncountable infinity of probabilistic features for optimal prediction. For processes generated by hidden Markov chains the consequences are…
In this study, a new extension of the Markov Renewal theory is introduced by allowing time to evolve in multiple dimensions. The resulting chains are referred to as multi-time Markov Renewal chains and since this extension is new, the state…
The asymptotic variance is an important criterion to evaluate the performance of Markov chains, especially for the central limit theorems. We give the variational formulas for the asymptotic variance of discrete-time (non-reversible) Markov…
Questions are posed regarding the influence that the column sums of the transition probabilities of a stochastic matrix (with row sums all one) have on the stationary distribution, the mean first passage times and the Kemeny constant of the…
In this paper, we first introduce and define several new information divergences in the space of transition matrices of finite Markov chains which measure the discrepancy between two Markov chains. These divergences offer natural…
For a network of discrete states with a periodically driven Markovian dynamics, we develop an inference scheme for an external observer who has access to some transitions. Based on waiting-time distributions between these transitions, the…
Consider a system evolving according to an absorbing discrete-time Markov chain with known transition matrix. The state of the system is observed at two points in time, separated by an unknown number of generations. We are interested in…
The accuracy of probability distributions inferred using machine-learning algorithms heavily depends on data availability and quality. In practical applications it is therefore fundamental to investigate the robustness of a statistical…
Markov chains are a natural and well understood tool for describing one-dimensional patterns in time or space. We show how to infer $k$-th order Markov chains, for arbitrary $k$, from finite data by applying Bayesian methods to both…
Markov chains for probability distributions related to matrix product states and 1D Hamiltonians are introduced. With appropriate 'inverse temperature' schedules, these chains can be combined into a random approximation scheme for ground…
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…
We develop a domain-theoretic framework for imprecise probability reasoning and inference on general topological spaces with a countably based continuous lattice of open sets. We address two distinct forms of uncertainty: partial or…
Nonlinear Markov chains with finite state space have been introduced in Kolokoltsov (2010). The characteristic property of these processes is that the transition probabilities do not only depend on the state, but also on the distribution of…