Related papers: Renewal stochastic processes with correlated event…
In many biological systems, chemical reactions or changes in a physical state are assumed to occur instantaneously. For describing the dynamics of those systems, Markov models that require exponentially distributed inter-event times have…
We consider a one-dimensional persisent random walk viewed as a deterministic process with a form of time reversal symmetry. Particle reservoirs placed at both ends of the system induce a density current which drives the system out of…
In the renewal processes, if the waiting time probability density function is a tempered power-law distribution, then the process displays a transition dynamics; and the transition time depends on the parameter $\lambda$ of the exponential…
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…
We study large deviations, over a long time window $T \to \infty$, of the dynamical observables $A_n = \int_{0}^{T} x^n(t) dt$, $n=3,4,\dots$, where $x(t)$ is a centered stationary Gaussian process in continuous time. We show that, for…
The first-passage time is proposed as an independent thermodynamic parameter of the statistical distribution that generalizes the Gibbs distribution. The theory does not include the determination of the first passage statistics itself. A…
A many-server queueing system is considered in which customers arrive according to a renewal process and have service and patience times that are drawn from two independent sequences of independent, identically distributed random variables.…
This paper presents a new numerical scheme for simulating stochastic processes specified by their marginal distribution functions and covariance functions. Stochastic samples are firstly generated to automatically satisfy target marginal…
We study systems of particles on a line which have a maximum, are locally finite and evolve with independent increments. ``Quasi-stationary states'' are defined as probability measures, on the \sigma-algebra generated by the gap variables,…
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…
Stochastic models of sequential mutation acquisition are widely used to quantify cancer and bacterial evolution. Across manifold scenarios, recurrent research questions are: how many cells are there with $n$ alterations, and how long will…
Statistical systems are conceived from the standpoint of statistical mechanics, as made of a (generally large) number of identical units and exhibiting a (generally large) number of different configurations (microstates), among which only…
This thesis is dedicated to the study of stochastic processes; non-deterministic physical phenomena that can be well described by classical physics. The stochastic processes we are interested in are akin to Brownian Motion and can be…
We give an introduction to phase transitions in the steady states of systems that evolve stochastically with equilibrium and nonequilibrium dynamics, the latter defined as those that do not possess a time-reversal symmetry. We try as much…
We use the model of ballistic deposition as a simple way to establish cooperation among the columns of a growing surface, \emph{the single individual of the same society}. We show that cooperation generates memory properties and at same…
Modelling the evolution of a system using stochastic dynamics typically implies a greater subjective uncertainty in the adopted system coordinates as time progresses, and stochastic entropy production has been developed as a measure of this…
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…
Point processes model the distribution of random point sets in mathematical spaces, such as spatial and temporal domains, with applications in fields like seismology, neuroscience, and economics. Existing statistical and machine learning…
We study a renewal problem within a periodic environment, departing from the classical renewal theory by relaxing the assumption of independent and identically distributed inter-arrival times. Instead, the conditional distribution of the…
We study time continuous branching processes with exponentially distributed lifetimes, with two types of cells that proliferate according to binary fission. A range of possible system dynamics are considered, each of which is characterized…