Related papers: On Discrete Time Prabhakar-Generalized Fractional …
We construct admissible circulant Laplacian matrix functions as generators for strictly increasing random walks on the integer line. These Laplacian matrix functions refer to a certain class of Bernstein functions. The approach has…
The effect of refractory periods in partial resetting processes is studied. Under Poissonian partial resets, a state variable jumps to a value closer to the origin by a fixed fraction at constant rate, $x\to a x$. Following each reset, a…
In many physical, social or economical phenomena we observe changes of a studied quantity only in discrete, irregularly distributed points in time. The stochastic process used by physicists to describe this kind of variables is the…
Time evolution in several classes of quantum devices is generated through the application of quantum gates. Resetting is a critical technological feature in these systems allowing for mid-circuit measurement and complete or partial qubit…
We review statistical properties of models generated by the application of a (positive and negative order) fractional derivative operator to a standard random walk and show that the resulting stochastic walks display slowly-decaying…
A multivariate fractional Poisson process was recently defined in Beghin and Macci (2016) by considering a common independent random time change for a finite dimensional vector of independent (non-fractional) Poisson processes; moreover it…
In this paper, we introduce drifted versions of the generalized counting process (GCP) with a deterministic drift and a random drift. The composition of stable subordinator with an independent inverse stable subordinator is taken as the…
In recent years, it has been well-established that adding a restart mechanism can alter the firstpassage statistics of a stochastic processes in useful and interesting ways. Though different mecha-nisms have been investigated, we derive a…
Fractional renewal processes as a generalization of Poisson process are already in the literature. In this paper, by introducing a new concept of generalized density function, the authors construct new fractional renewal processes in the…
We consider the Reinforcement Learning problem of controlling an unknown dynamical system to maximise the long-term average reward along a single trajectory. Most of the literature considers system interactions that occur in discrete time…
In this paper we introduce the space-fractional Poisson process whose state probabilities $p_k^\alpha(t)$, $t>0$, $\alpha \in (0,1]$, are governed by the equations $(\mathrm d/\mathrm dt)p_k(t) = -\lambda^\alpha (1-B)p_k^\alpha(t)$, where…
The fractional Poisson process and the Wright process (as discretization of the stable subordinator) along with their diffusion limits play eminent roles in theory and simulation of fractional diffusion processes. Here we have analyzed…
Due to wide applications in diverse fields, random walks subject to stochastic resetting have attracted considerable attention in the last decade. In this paper, we study discrete-time random walks on complex network with multiple resetting…
The aim of this paper is the analysis of the fractional Poisson process where the state probabilities $p_k^{\nu_k}(t)$, $t\ge 0$, are governed by time-fractional equations of order $0<\nu_k\leq 1$ depending on the number $k$ of events…
In many complex systems studied in statistical physics, inter-arrival times between events such as solar flares, trades and neuron voltages follow a heavy-tailed distribution. The set of event times is fractal-like, being dense in some time…
The stochastic trajectories of molecules in living cells, as well as the dynamics in many other complex systems, often exhibit memory in their path over long periods of time. In addition, these systems can show dynamic heterogeneities due…
We consider renewal stochastic processes generated by non-independent events from the perspective that their basic distribution and associated generating functions obey the statistical-mechanical structure of systems with interacting…
We consider time-changed Poisson processes, and derive the governing difference-differential equations (DDE) these processes. In particular, we consider the time-changed Poisson processes where the the time-change is inverse Gaussian, or…
Random fields are useful mathematical tools for representing natural phenomena with complex dependence structures in space and/or time. In particular, the Gaussian random field is commonly used due to its attractive properties and…
Time evolutions whose infinitesimal generator is a fractional time derivative arise generally in the long time limit. Such fractional time evolutions are considered here for random walks. An exact relationship is given between the…