相关论文: Microcanonical conditioning of Markov processes on…

We study time-changed Markov processes to speed up the convergence of Markov chain Monte Carlo (MCMC) algorithms. The time-changed process is defined by adjusting the speed of time of a base process via a user-chosen, state-dependent…

This paper studies: (i) the long time behaviour of the empirical distribution of age and normalised position of an age dependent critical branching Markov process conditioned on non-extinction; and (ii) the super-process limit of a sequence…

A discrete-time Markov chain can be transformed into a new Markov chain by looking at its states along iterations of an almost surely finite stopping time. By the optional stopping theorem, any bounded harmonic function with respect to the…

We consider general Markov chains with discrete time in an arbitrary measurable (phase) space and homogeneous in time. Markov chains are defined by the classical transition function which within the framework of the operator treatment…

We present a class of stochastic processes in which the large deviation functions of time-integrated observables exhibit singularities that relate to dynamical phase transitions of trajectories. These illustrative examples include Brownian…

We consider a general honest homogeneous continuous-time Markov process with restarts. The process is forced to restart from a given distribution at time moments generated by an independent Poisson process. The motivation to study such…

In the context of time-subordinated Brownian motion models, Fourier theory and methodology are proposed to modelling the stochastic distribution of time increments. Gaussian Variance-Mean mixtures and time-subordinated models are reviewed…

We consider the model of Brownian motion indexed by the Brownian tree, which has appeared in a variety of different contexts in probability, statistical physics and combinatorics. For this model, the total occupation measure is known to…

In the paper we study continuous time controlled Markov processes using discrete time controlled Markov processes. We consider long run functionals: average reward per unit time or long run risk sensitive functional. We also investigate…

Since the classical work of L\'evy, it is known that the local time of Brownian motion can be characterized through the limit of level crossings. While subsequent extensions of this characterization have primarily focused on Markovian or…

The Kramers-Moyal analysis is a well established approach to analyze stochastic time series from complex systems. If the sampling interval of a measured time series is too low, systematic errors occur in the analysis results. These errors…

We study Markov processes where the "time" parameter is replaced by paths in a directed graph from an initial vertex to a terminal one. Along each directed path the process is Markov and has the same distribution as the one along any other…

These notes give a summary of techniques used in large deviation theory to study the fluctuations of time-additive quantities, called dynamical observables, defined in the context of Langevin-type equations, which model equilibrium and…

This paper considers a Markovian model of a limit order book where time-dependent rates are allowed. With the objective of understanding the mechanisms through which a microscopic model of an orderbook can converge to more general diffusion…

We show that stochastic processes with linear conditional expectations and quadratic conditional variances are Markov, and their transition probabilities are related to a three-parameter family of orthogonal polynomials which generalize the…

Our purpose is to investigate properties for processes with stationary and independent increments under $G$-expectation. As applications, we prove the martingale characterization to $G$-Brownian motion and present a decomposition for…

Continuous-time Markov chains are mathematical models that are used to describe the state-evolution of dynamical systems under stochastic uncertainty, and have found widespread applications in various fields. In order to make these models…

The analysis of local minima in time series data and random landscapes is essential across numerous scientific disciplines, offering critical insights into system dynamics. Recently, Kundu, Majumdar, and Schehr derived the exact…

We consider a class of optimal control problems, with finite or infinite horizon, for a continuous-time Markov chain with finite state space. In this case, the control process affects the transition rates. We suppose that the controlled…

We study a new technique for the asymptotic analysis of heavy-tailed systems conditioned on large deviations events. We illustrate our approach in the context of ruin events of multidimensional regularly varying random walks. Our approach…