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We are studying stationary random processes with conditional polynomial moments that allow a continuous path modification. Processes with continuous path modification, are important because they are relatively easy to simulate. One does not…

Probability · Mathematics 2024-11-21 Paweł J. Szabłowski

In this short note we consider semi-Markov processes satisfying the condition of direction-time independence (Markov renewal processes). We derive large deviation principles and fluctuation theorems for the empirical current and the…

Statistical Mechanics · Physics 2017-09-19 A. Faggionato

Suppose $ E$ is a space with a null-recurrent Markov kernel $ P$. Furthermore, suppose there are infinite particles with variable weights on $ E$ performing a random walk following $ P$. Let $ X_{t}$ be a weighted functional of the position…

Probability · Mathematics 2010-12-01 Souvik Ghosh

Markov automata combine non-determinism, probabilistic branching, and exponentially distributed delays. This compositional variant of continuous-time Markov decision processes is used in reliability engineering, performance evaluation and…

Logic in Computer Science · Computer Science 2017-05-11 Tim Quatmann , Sebastian Junges , Joost-Pieter Katoen

We study the stationary fluctuations of independent run-and-tumble particles. We prove that the joint densities of particles with given internal state converges to an infinite dimensional Ornstein-Uhlenbeck process. We also consider an…

Probability · Mathematics 2024-03-13 Frank Redig , Hidde van Wiechen

We consider a one-dimensional piecewise deterministic Markov process (PDMP) on $[0,1]$ with resetting at $0$ and depending on a small parameter $\varepsilon>0$. In the singular vanishing limit $\varepsilon \to 0$ we prove that the ``…

Probability · Mathematics 2025-12-23 Cédric Bernardin , Vsevolod Vladimirovich Tarsamaev

Renewal processes with heavy-tailed power law distributed sojourn times are commonly encountered in physical modelling and so typical fluctuations of observables of interest have been investigated in detail. To describe rare events the rate…

Statistical Mechanics · Physics 2018-10-26 Wanli Wang , Johannes H. P. Schulz , Weihua Deng , Eli Barkai

We present and establish large deviations principles for general multivariate renewal-reward processes associated with a classical discrete-time renewal process. A renewal-reward process describes a cumulative reward over time, supposing…

Mathematical Physics · Physics 2019-04-11 Marco Zamparo

Although resetting has widespread applicability, applying it to the dynamics in the presence of spatial quenched disorder, which is essential in many physical problems, is challenging. In this study, we consider a well-known one-dimensional…

Statistical Mechanics · Physics 2026-04-06 Riya Verma , Binayak Banerjee , Shamik Gupta , Saroj Kumar Nandi

A common and effective method for calculating the steady-state distribution of a process under stochastic resetting is the renewal approach that requires only the knowledge of the reset-free propagator of the underlying process and the…

Statistical Mechanics · Physics 2024-11-15 Ron Vatash , Amy Altshuler , Yael Roichman

We address the general problem of formulating the dynamical large deviations of non-Markovian systems in a closed form. Specifically, we consider a broad class of ``self-interacting'' jump processes whose dynamics depends on the past…

Statistical Mechanics · Physics 2026-03-25 Francesco Coghi , Amarjit Budhiraja , Juan P. Garrahan

Recursive stochastic algorithms have gained significant attention in the recent past due to data driven applications. Examples include stochastic gradient descent for solving large-scale optimization problems and empirical dynamic…

Machine Learning · Computer Science 2020-07-27 Abhishek Gupta , Hao Chen , Jianzong Pi , Gaurav Tendolkar

Stochastic resetting can be naturally understood as a renewal process governing the evolution of an underlying stochastic process. In this work, we formally derive well-known results of diffusion with resets from a renewal theory…

Statistical Mechanics · Physics 2022-10-05 Axel Masó-Puigdellosas , Daniel Campos , Vicenç Méndez

Stochastic processes under resetting at random times have attracted a lot of attention in recent years and served as illustrations of nontrivial and interesting static and dynamic features of stochastic dynamics. In this paper, we aim to…

Statistical Mechanics · Physics 2025-06-18 Yating Wang , Hanshuang Chen

The large deviations at various levels that are explicit for Markov jump processes satisfying detailed-balance are revisited in terms of the supersymmetric quantum Hamiltonian $H$ that can be obtained from the Markov generator via a…

Statistical Mechanics · Physics 2024-07-15 Cecile Monthus

We consider a random walk in random environment with random holding times, that is, the random walk jumping to one of its nearest neighbors with some transition probability after a random holding time. Both the transition probabilities and…

Probability · Mathematics 2014-12-30 Ryoki Fukushima , Naoki Kubota

We consider the maximum entropy Markov chain inference approach to characterize the collective statistics of neuronal spike trains, focusing on the statistical properties of the inferred model. We review large deviations techniques useful…

Neurons and Cognition · Quantitative Biology 2018-08-15 Rodrigo Cofre , Cesar Maldonado , Fernando Rosas

The purpose of this paper is to ensure the conditions of G\"artner-Ellis Theorem for evaluations of the empirical measure. We show that up-to-date conditions for ensuring the convergence to a quasi-stationary distribution can be applied…

Probability · Mathematics 2020-04-21 Aurélien Velleret

We consider time-continuous Markovian discrete-state dynamics on random networks of interacting agents and study the large population limit. The dynamics are projected onto low-dimensional collective variables given by the shares of each…

Probability · Mathematics 2026-03-19 Marvin Lücke , Jobst Heitzig , Péter Koltai , Nora Molkenthin , Stefanie Winkelmann

Proper management of resources whose arrival and consumption are subject to environmental randomness is an intrinsic process in both natural and artificial systems. This phenomenon can be modeled as a queuing process whose arrival…

Statistical Mechanics · Physics 2026-05-18 José Giral-Barajas , Paul C. Bressloff