A fast algorithm for the first-passage times of Gauss-Markov processes with Hölder continuous boundaries

DOI10.1007/s10955-010-0033-6zbMath1339.60098OpenAlexW1980181762MaRDI QIDQ643719

Marcelo O. Magnasco, Thibaud Taillefumier

Publication date: 2 November 2011

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10955-010-0033-6

zbMATH Keywords

stochastic differential equationsOrnstein-Uhlenbeck processnumerical algorithmGauss-Markov processesfirst-passage times

Mathematics Subject Classification ID

Gaussian processes (60G15) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Diffusion processes (60J60) Sample path properties (60G17) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

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Cites Work

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• The Ornstein-Uhlenbeck process as a model for neuronal activity. I. Mean and variance of the firing time
• A Haar-like construction for the Ornstein Uhlenbeck process
• A review of the methods for signal estimation in stochastic diffusion leaky integrate-and-fire neuronal models
• Diffusion approximation of the neuronal model with synaptic reversal potentials
• The Fokker-Planck equation. Methods of solution and applications.
• An integral algorithm for numerical integration of one-dimensional additive colored noise problems
• A Monte Carlo method for the simulation of first passage times of diffusion processes
• Weak approximation of killed diffusion using Euler schemes.
• A correction note on the first passage time of an Ornstein-Uhlenbeck process to a boundary
• A review of the integrate-and-fire neuron model: II. Inhomogeneous synaptic input and network properties
• A review of the integrate-and-fire neuron model: I. Homogeneous synaptic input
• Computing the first passage time density of a time-dependent Ornstein-Uhlenbeck process to a moving boundary
• Exact approximation rate of killed hypoelliptic diffusions using the discrete Euler scheme
• Simulation of jump diffusions and the pricing of options
• Exact solutions of the Fokker-Planck equations with moving boundaries
• Crossing probabilities for diffusion processes with piecewise continuous boundaries
• Boundary crossing probability for Brownian motion
• Estimation of the input parameters in the Feller neuronal model
• First passage time for multivariate jump-diffusion processes in finance and other areas of applications
• Canonical representations of Gaussian processes and their applications
• First-passage-time density and moments of the ornstein-uhlenbeck process
• Boundary crossing probability for Brownian motion and general boundaries
• Variable Step Size Control in the Numerical Solution of Stochastic Differential Equations
• Smoothness of first passage time distributions and a new integral equation for the first passage time density of continuous Markov processes
• Stepsize Control for Mean-Square Numerical Methods for Stochastic Differential Equations with Small Noise
• Representations of the First Hitting Time Density of an Ornstein-Uhlenbeck Process¹
• An Explicit Representation of a Stationary Gaussian Process
• Heuristic Approach to the Kolmogorov-Smirnov Theorems
• On the First Passage Time Probability Problem

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