Related papers: Damped jump-telegraph processes
This paper considers differential problems with random switching, with specific applications to the motion of cells and centrally coordinated motion. Starting with a differential-equation model of cell motion that was proposed previously,…
A one-dimensional run-and-tumble particle (RTP) switches randomly between a left and right moving state of constant speed $v$. This type of motion arises in a wide range of applications in cell biology, including the unbiased growth and…
We study the dynamics of a radioactive species flowing through a porous material, within the Continuous-Time Random Walk (CTRW) approach to the modelling of stochastic transport processes. Emphasis is given to the case where radioactive…
We show that the occurrence of chaotic diffusion in a typical class of time-delayed systems with linear instantaneous and nonlinear delayed term can be well described by an anti-persistent random walk. We numerically investigate the…
For $\lambda>0$, we define a $\lambda$-damped random walk to be a random walk that is started from a random vertex of a graph and stopped at each step with probability $\frac{\lambda}{1+\lambda}$, otherwise continued with probability…
We consider a new model of quantum walk on a one-dimensional momentum space that includes both discrete jumps and continuous drift. Its time evolution has two stages; a Markov diffusion followed by localized dynamics. As in the well known…
Simulation methods based on stochastic realizations of state vector evolutions are commonly used tools to solve open quantum system dynamics, both in the Markovian and non-Markovian regime. Here, we address the question of waiting time…
We study decentralized learning over networks where data are distributed across nodes without a central coordinator. Random walk learning is a token-based approach in which a single model is propagated across the network and updated at each…
The diffusion of a walk in the presence of traps is investigated. Different diffusion regimes are obtained considering the magnitude of the fluctuations in waiting times and jump distances. A constant velocity during the jump motion is…
In a continuous time random walk (CTRW), each random jump follows a random waiting time. CTRW scaling limits are time-changed processes that model anomalous diffusion. The outer process describes particle jumps, and the non-Markovian inner…
We consider Markov processes, which describe e.g. queueing network processes, in a random environment which influences the network by determining random breakdown of nodes, and the necessity of repair thereafter. Starting from an explicit…
The parameters of a discrete stationary Markov model are transition probabilities between states. Traditionally, data consist in sequences of observed states for a given number of individuals over the whole observation period. In such a…
We consider Piecewise Deterministic Markov Processes (PDMPs) with a finite set of discrete states. In the regime of fast jumps between discrete states, we prove a law of large number and a large deviation principle. In the regime of fast…
In this paper, we consider a type of continuous time random walk model where the jump length is correlated with the waiting time. The asymptotic behaviors of the coupled jump probability density function in the Fourier-Laplace domain are…
We propose a novel, tractable latent state inference scheme for Markov jump processes, for which exact inference is often intractable. Our approach is based on an entropic matching framework that can be embedded into the well-known…
Multi-agent systems can be successfully described by kinetic models, which allow one to explore the large scale aggregate trends resulting from elementary microscopic interactions. The latter may be formalised as collision-like rules, in…
We treat the class of universal Markov processes on the d-dimensional Euklidean space which do not depend on random. For these, as well as for several subclasses, we prove criteria whether a function f, defined on the positive half-line,…
We consider a random walk with a negative drift and with a jump distribution which under Cram\'er's change of measure belongs to the domain of attraction of a spectrally positive stable law. If conditioned to reach a high level and suitably…
We are interested in the connection between a metastable continuous state space Markov process (satisfying e.g. the Langevin or overdamped Langevin equation) and a jump Markov process in a discrete state space. More precisely, we use the…
We consider random walks on the support of a random purely atomic measure on $\mathbb{R}^d$ with random jump probability rates. The jump range can be unbounded. The purely atomic measure is reversible for the random walk and stationary for…