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In this paper we consider discrete and continuous time risk sensitive optimal stopping problem. Using suitable properties of the underlying Feller-Markov process we prove continuity of the optimal stopping value function and provide formula…
For discrete-time stochastic processes, there is a close connection between return/waiting times and entropy. Such a connection cannot be straightforwardly extended to the continuous-time setting. Contrarily to the discrete-time case one…
Before delegating a task to an autonomous system, a human operator may want a guarantee about the behavior of the system. This paper extends previous work on conformal prediction for functional data and conformalized quantile regression to…
Let $X$ be a symmetric strong Markov process on a Luzin space. In this paper, we present criteria of the $L^p$-independence of spectral bounds for generalized non-local Feynman-Kac semigroups of $X$ that involve continuous additive…
In this paper we study the Markov-modulated M/M/$\infty$ queue, with a focus on the correlation structure of the number of jobs in the system. The main results describe the system's asymptotic behavior under a particular scaling of the…
Many problems of practical interest rely on Continuous-time Markov chains~(CTMCs) defined over combinatorial state spaces, rendering the computation of transition probabilities, and hence probabilistic inference, difficult or impossible…
In this paper, we study the problem of estimating the autocovariance sequence resulting from a reversible Markov chain. A motivating application for studying this problem is the estimation of the asymptotic variance in central limit…
Motivated by queues with many servers, we study Brownian steady-state approximations for continuous time Markov chains (CTMCs). Our approximations are based on diffusion models (rather than a diffusion limit) whose steady-state, we prove,…
For a Tychonoff space $X$, we denote by $C_p(X)$ the space of all real-valued continuous functions on $X$ with the topology of pointwise convergence. We give the functional characterization of the covering property of Hurewicz.
The literature on continuous-time stochastic optimal control seldom deals with the case of discrete state spaces. In this paper, we provide a general framework for the optimal control of continuous-time Markov chains on finite graphs. In…
Adaptive Monte Carlo methods can be viewed as implementations of Markov chains with infinite memory. We derive a general condition for the convergence of a Monte Carlo method whose history dependence is contained within the simulated…
In this paper, we derive (local) orthogonality graphs for the popular continuous-time state space models, including in particular multivariate continuous-time ARMA (MCARMA) processes. In these (local) orthogonality graphs, vertices…
We find the asymptotic distribution of the sample autocovariances of long-memory processes in cases of finite and infinite fourth moment. Depending on the interplay of assumptions on moments and the intensity of dependence, there are three…
In this paper, we show that for discrete time-varying linear control systems uniform complete controllability implies arbitrary assignability of dichotomy spectrum of closed-loop systems. This result significantly strengthens the result in…
What limits how fast a Lyapunov function can decay under input bounds? We address this question by showing how the shape of Lyapunov comparison functions governs guaranteed decay for control affine systems. Using a windowed nominal…
Reactivity, contractivity, and Lyapunov exponents are powerful tools for studying the stability properties of dynamical systems and have been extensively investigated in the literature for decades. In this paper, we review and extend the…
We consider regular lattices of coupled chaotic maps. Depending on lattice size, there may exist a window in parameter space where complete synchronization is eventually attained after a transient regime. Close outside this window, an…
We give characterizations of unital uniform topological algebras and saturated locally multiplicatively convex algebras by means of multiplicative linear functionals. Some automatic continuity theorems in advertibly complete uniform…
Application of CTRW to dipole hopping transport is considered. Correct versions of derivation of the CTRW-equations are presented. Existence of different forms of memory kernels is demonstrated. Correction of Scher-Lax memory kernel within…
The stability of stochastic Model Predictive Control (MPC) subject to additive disturbances is often demonstrated in the literature by constructing Lyapunov-like inequalities that guarantee closed-loop performance bounds and boundedness of…