On the M/M/1 Queue with Catastrophes and Its Continuous Approximation
For the M/M/1 queue in the presence of catastrophes the transition probabilities, densities of
the busy period and of the catastrophe waiting time are determined. A heavy-traffic …
the busy period and of the catastrophe waiting time are determined. A heavy-traffic …
Dynamical large deviations of reflected diffusions
J du Buisson, H Touchette - Physical Review E, 2020 - APS
We study the large deviations of time-integrated observables of Markov diffusions that have
perfectly reflecting boundaries. We discuss how the standard spectral approach to …
perfectly reflecting boundaries. We discuss how the standard spectral approach to …
A double-ended queue with catastrophes and repairs, and a jump-diffusion approximation
Consider a system performing a continuous-time random walk on the integers, subject to
catastrophes occurring at constant rate, and followed by exponentially-distributed repair …
catastrophes occurring at constant rate, and followed by exponentially-distributed repair …
Standard and fractional reflected Ornstein–Uhlenbeck processes as the limits of square roots of Cox–Ingersoll–Ross processes
Y Mishura, A Yurchenko-Tytarenko - Stochastics, 2023 - Taylor & Francis
In this paper, we establish a new connection between Cox–Ingersoll–Ross (CIR) and
reflected Ornstein–Uhlenbeck (ROU) models driven by either a standard Wiener process or …
reflected Ornstein–Uhlenbeck (ROU) models driven by either a standard Wiener process or …
On the probability densities of an Ornstein–Uhlenbeck process with a reflecting boundary
LM Ricciardi, L Sacerdote - Journal of Applied Probability, 1987 - cambridge.org
We show that the transition pdf of the Ornstein–Uhlenbeck process with a reflection
condition at an assigned state S is related by integral-type equations to the free transition …
condition at an assigned state S is related by integral-type equations to the free transition …
Modeling COVID-19 pandemic with financial markets models: The case of Ja\'en (Spain)
J Guerrero, MC Galiano, G Orlando - arxiv preprint arxiv:2301.08803, 2023 - arxiv.org
The main objective of this work is to test whether some stochastic models typically used in
financial markets could be applied to the COVID-19 pandemic. To this end we have …
financial markets could be applied to the COVID-19 pandemic. To this end we have …
Diffusion approximation to a queueing system with time-dependent arrival and service rates
A Di Crescenzo, AG Nobile - Queueing systems, 1995 - Springer
A time nonhomogeneous diffusion approximation to a single server-single queue service
system is obtained. Under various assumptions on the time-dependent functions appearing …
system is obtained. Under various assumptions on the time-dependent functions appearing …
Stochastic population theory: birth and death processes
LM Ricciardi - Mathematical Ecology: An Introduction, 1986 - Springer
Birth and death processes were introduced by Feller (1939) and have since been used as
models for population growth, queue formation, in epidemiology and in many other areas of …
models for population growth, queue formation, in epidemiology and in many other areas of …
Diffusion approximation and first-passage-time problem for a model neuron: III. A birth-and-death process approach
A stochastic model for single neuron's activity is constructed as the continuous limit of a birth-
and-death process in the presence of a reversal hyper-polarization potential. The resulting …
and-death process in the presence of a reversal hyper-polarization potential. The resulting …
The first passage time problem for Gauss-diffusion processes: algorithmic approaches and applications to LIF neuronal model
A Buonocore, L Caputo, E Pirozzi… - … and Computing in Applied …, 2011 - Springer
Motivated by some unsolved problems of biological interest, such as the description of firing
probability densities for Leaky Integrate-and-Fire neuronal models, we consider the first …
probability densities for Leaky Integrate-and-Fire neuronal models, we consider the first …