[PDF][PDF] Exact solutions and asymptotic behaviors for the reflected Wiener, Ornstein-Uhlenbeck and Feller diffusion processes

V Giorno, AG Nobile - Mathematical Biosciences and …, 2023 - aimspress.com
… A detailed study of the moments of first-passage time and of … can be interpreted as the neuronal
reversal hyperpolarization … of the Wiener process and of the Ornstein-Uhlenbeck process

Efficient numerical approximation of a non-regular Fokker–Planck equation associated with first-passage time distributions

U Boehm, S Cox, G Gantner, R Stevenson - BIT Numerical Mathematics, 2022 - Springer
… a one-dimensional stochastic differential equation is assumed to describe the difference in
activity of two competing neuronmethod we introduce is also relevant for other applications. …

Reflecting stochastic dynamics of active-passive populations with applications in operations research and neuroscience

TKT Thieu, R Melnik - arXiv preprint arXiv:2102.07766, 2021 - arxiv.org
… We provide details of the queueing theory and neuronal models … first passage time method
for a two dimensional Ornstein-… equivalent to the OrnsteinUhlenbeck process from statistical …

Continuous‐time multi‐type Ehrenfest model and related OrnsteinUhlenbeck diffusion on a star graph

A Di Crescenzo, B Martinucci… - … Methods in the Applied …, 2022 - Wiley Online Library
… based on the OrnsteinUhlenbeck process. The state space of … and variance of the first-passage
time through a constant … neuronal model and Buonocore et al 21 for applications in …

An inverse problem for the first-passage place of some diffusion processes with random starting point

M Abundo - Stochastic Analysis and Applications, 2020 - Taylor & Francis
first-passage times of jump-diffusions X(t) (see eg [Citation2–4], and references therein); in
([Citation5]) it was considered the problem of computing the first-passage time of … process with …

Kac-Ornstein-Uhlenbeck processes: stationary distributions and exponential functionals

N Ratanov - Methodology and Computing in Applied Probability, 2022 - Springer
Ornstein-Uhlenbeck processes whose parameters are modulated by an external two-state
Markov process. … Some results in terms of first passage distributions with applications to neural

Applications of an extended geometric Brownian motion degradation model

YS Hsu, PC Chen, MY Lee, CH Wu - … Statistics-Theory and Methods, 2022 - Taylor & Francis
… We determine the convergence behavior of the first passage time as the random … 3 2 e − b
2 s 2 ϵ 2 d s < ∞ … The sample distribution of { T ϵ , y , i } i = 1 n remains the inverse Gaussian …

Learning physical properties of anomalous random walks using graph neural networks

H Verdier, M Duval, F Laurent, A Cassé… - Journal of Physics A …, 2021 - iopscience.iop.org
… particle trajectories is the inverse problem of inferring the … 'excursions' [22], or of first passage
time statistics [23]. Others are … of the approach, challenges in its application to experimental …

A Review of Stochastic Models of Neuronal Dynamics: From a Single Neuron to Networks

MF Carfora - International Symposium on Mathematical and …, 2022 - Springer
… a first passage time (FPT) problem for a stochastic OU process… approximations; numerical
techniques to evaluate this … : Algorithmic approaches and applications to LIF neuronal

Non-equilibrium thermodynamics with first-passage time of states as independent thermodynamic parameter

VV Ryazanov - arXiv preprint arXiv:2003.08307, 2020 - arxiv.org
… In our approach lifetime is understood as complete lifetime, … In [12, 35] the possibilities of
applying distributions with a … thermodynamics [2-4], in which flows, quantities inverse to the …