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In this paper, we consider the gradual-impulse control problem of continuous-time Markov decision processes, where the system performance is measured by the expectation of the exponential utility of the total cost. We prove, under very…

Adaptive dynamical systems arise in a multitude of contexts, e.g., optimization, control, communications, signal processing, and machine learning. A precise characterization of their fundamental limitations is therefore of paramount…

We consider stochastic thermodynamics as a theory of statistical inference for experimentally observed fluctuating time-series. To that end, we introduce a general framework for quantifying the knowledge about the dynamical state of the…

Change of measures has been an effective method in stochastic control and analysis; in continuous-time control this follows Girsanov's theorem applied to both fully observed and partially observed models, in decentralized stochastic control…

Piecewise-deterministic Markov processes combine continuous in time dynamics with jump events, the rates of which generally depend on the continuous variables and thus are not constants. This leads to a problem in a Monte-Carlo simulation…

Markov models are widely used to describe processes of stochastic dynamics. Here, we show that Markov models are a natural consequence of the dynamical principle of Maximum Caliber. First, we show that when there are different possible…

A novel class of non-reversible Markov chain Monte Carlo schemes relying on continuous-time piecewise-deterministic Markov Processes has recently emerged. In these algorithms, the state of the Markov process evolves according to a…

In this paper we consider the classical differential equations of Hodgkin and Huxley and a natural refinement of them to include a layer of stochastic behavior, modeled by a large number of finite-state-space Markov processes coupled to a…

We consider a continuous-time financial market with an asset whose price is modeled by a linear stochastic differential equation with drift and volatility switching driven by a uniformly ergodic jump Markov process with a countable state…

In the present paper, we give some examples of stochastic differential equations which have delicateness in the Markov and strong Markov properties, the uniqueness locally in time and globally in time, and initial conditions. Moreover, we…

When analysing statistical systems or stochastic processes, it is often interesting to ask how they behave given that some observable takes some prescribed value. This conditioning problem is well understood within the linear operator…

In a series of works published in the 1990-s, Kerov put forth various applications of the circle of ideas centred at the Markov moment problem to the limiting shape of random continual diagrams arising in representation theory and spectral…

Continuous time financial market models are often motivated as scaling limits of discrete time models. The objective of this paper is to establish such a connection for a robust framework. More specifically, we consider discrete time models…

In this article we discuss several aspects of the stochastic dynamics of spin models. The paper has two independent parts. Firstly, we explore a few properties of the multi-point correlations and responses of generic systems evolving in…

We formulate a data-driven method for constructing finite volume discretizations of a dynamical system's underlying Continuity / Fokker-Planck equation. A method is employed that allows for flexibility in partitioning state space,…

We solve two problems related to the fluctuations of time-integrated functionals of Markov diffusions, used in physics to model nonequilibrium systems. In the first we derive and illustrate the appropriate boundary conditions on the…

In this paper, we equip the conventional discrete-time queueing network with a Markovian input process, that, in addition to the usual short-term stochastics, governs the mid- to long-term behavior of the links between the network nodes.…

Although the notion of diagnostic problem has been extensively investigated in the context of static systems, in most practical applications the behavior of the modeled system is significantly variable during time. The goal of the paper is…

The inference of Markov models from data on stochastic dynamical trajectories over the large time-window $T$ is revisited via the Large Deviations at Level 2.5 for the time-empirical density and the time-empirical flows. The goal is to…

We develop a general theory dealing with stochastic models for dynamical systems that are governed by various nonlinear, ordinary or partial differential, equations. In particular, we address the problem how flows in the random medium…