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We consider random walks on marked simple point processes with symmetric jump rates and unbounded jump range. We prove homogenization properties of the associated Markov generators. As an application, we derive the hydrodynamic limit of the…
We present a simple derivation of a Feynman-Kac type formula to study fermionic systems. In this approach the real time or the imaginary time dynamics is expressed in terms of the evolution of a collection of Poisson processes. A computer…
In this paper, we aim to provide probabilistic and combinatorial insights into tree formulas for the Green function and hitting probabilities of Markov chains on a finite state space. These tree formulas are closely related to loop-erased…
The use of stochastic models, in effect piecewise deterministic Markov processes (PDMP), has become increasingly popular especially for the modeling of chemical reactions and cell biophysics. Yet, exact simulation methods, for the…
The dynamics of a non-Markovian open quantum system described by a general time-local master equation is studied. The propagation of the density operator is constructed in terms of two processes: (i) deterministic evolution and (ii)…
In order to give quantitative estimates for approximating the ergodic limit, we investigate probabilistic limit behaviors of time-averaging estimators of numerical discretizations for a class of time-homogeneous Markov processes, by…
We consider a risk model with a counting process whose intensity is a Markovian shot-noise process, to resolve one of the disadvantages of the Cram\'er-Lundberg model, namely the constant jump intensity of the Poisson process. Due to this…
We consider the stochastic ranking process with the jump times of the particles determined by Poisson random measures. We prove that the joint empirical distribution of scaled position and intensity measure converges almost surely in the…
We obtain non-Gaussian limit laws for one-dimensional random walk in a random environment assuming that the environment is a function of a stationary Markov process. This is an extension of the work of Kesten, M. Kozlov and Spitzer for…
The problem of parameter estimation by observations of inhomogeneous Poisson processes is considered. The method of moments estimator is studied and its stochastic expansion is obtained. This stochastic expansion is then used to obtain the…
We study a system of two non-interacting quantum wires with fermions of opposite chirality with a point contact junction at the origin across which tunneling can take place when an arbitrary time-dependent bias between the wires is applied.…
We consider a piecewise-deterministic Markov process governed by a jump intensity function, a rate function that determines the behaviour between jumps, and a stochastic kernel describing the conditional distribution of jump sizes. We study…
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 study properties of a subclass of Markov processes that have all moments that are continuous functions of the time parameter and more importantly are characterized by the property that say their $n-$th conditional moment given the past…
The transient dynamics of quantum coherence of Gaussian states are investigated. The state is coupled to an external environment which can be described by a Fano-Anderson type Hamiltonian. Solving the quantum Langevin equation, we obtain…
Modern methods of simulating molecular systems are based on the mathematical theory of Markov operators with a focus on autonomous equilibrated systems. However, non-autonomous physical systems or non-autonomous simulation processes are…
In most sampling algorithms, including Hamiltonian Monte Carlo, transition rates between states correspond to the probability of making a transition in a single time step, and are constrained to be less than or equal to 1. We derive a…
We consider the intensity-based approach for the modeling of default times of one or more companies. In this approach the default times are defined as the jump times of a Cox process, which is a Poisson process conditional on the…
In this paper, a study of random times on filtered probability spaces is undertaken. The main message is that, as long as distributional properties of optional processes up to the random time are involved, there is no loss of generality in…
In this paper we propose a new method for approximating the nonstationary moment dynamics of one dimensional Markovian birth-death processes. By expanding the transition probabilities of the Markov process in terms of Poisson-Charlier…