Boundary-Crossing Identities for Diffusions Having the??Time-Inversion Property, Journal of Theoretical Probability, vol.31, issue.2, pp.65-84, 2010. ,
DOI : 10.1007/s10959-009-0245-3
A neuronal modeling paradigm in the presence of refractoriness, Biosystems, vol.67, issue.1-3, pp.35-43, 2002. ,
DOI : 10.1016/S0303-2647(02)00061-8
A new integral equation for the evaluation of first-passage-time probability densities, Advances in Applied Probability, pp.784-800, 1987. ,
A Review of the Integrate-and-fire Neuron Model: I. Homogeneous Synaptic Input, Biological Cybernetics, vol.68, issue.1, pp.1-19, 2006. ,
DOI : 10.1007/s00422-006-0068-6
Hitting Times of Bessel Processes, Potential Analysis, vol.25, issue.2, pp.753-786, 2013. ,
DOI : 10.1007/s11118-012-9296-7
First passage times and sojourn times for Brownian motion in space and the exact Hausdorff measure of the sample path, Transactions of the American Mathematical Society, vol.103, issue.3, pp.434-450, 1962. ,
DOI : 10.1090/S0002-9947-1962-0143257-8
The minimum of a stationary Markov process superimposed on a U-shaped trend, Journal of Applied Probability, vol.2, issue.02, pp.399-408, 1969. ,
DOI : 10.1214/aoms/1177728918
Approximating the First Crossing-Time Density for a Curved Boundary, Bernoulli, vol.2, issue.2, pp.133-143, 1996. ,
DOI : 10.2307/3318547
Hitting time for Bessel processes -Walk on Moving Spheres Algorithm (WoMS) The Annals of Applied Probability, pp.2259-2289, 2013. ,
Non-Uniform Random Variate Generation, 1986. ,
DOI : 10.1007/978-1-4613-8643-8
The first-passage density of a continuous gaussian process to a general boundary, Journal of Applied Probability, vol.63, issue.01, pp.99-122, 1985. ,
DOI : 10.2307/3212169
The first-passage density of the Brownian motion process to a curved boundary, Journal of Applied Probability, vol.3, issue.02, pp.291-304, 1992. ,
DOI : 10.2307/3213751
The tangent approximation to one-sided Brownian exit densities, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.13, issue.3, pp.309-326, 1982. ,
DOI : 10.1007/BF00539832
An asymptotic expansion for one-sided Brownian exit densities, Zeitschrift f??r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.13, issue.1, pp.1-15, 1983. ,
DOI : 10.1007/BF00534172
Spiking neuron models: Single neurons, populations, plasticity, 2002. ,
DOI : 10.1017/CBO9780511815706
On the evaluation of first-passage-time probability densities via non-singular integral equations, Advances in Applied Probability, vol.22, issue.01, pp.20-36, 1989. ,
DOI : 10.2307/1969318
Sch??ma d'Euler continu pour des diffusions tu??es et options barri??re, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.326, issue.12, pp.1411-1414, 1998. ,
DOI : 10.1016/S0764-4442(98)80402-3
Weak approximation of killed diffusion using Euler schemes. Stochastic Process, Appl, vol.87, issue.2, pp.167-197, 2000. ,
Euler schemes and half-space approximation for the simulation of diffusion in a domain, ESAIM: Probability and Statistics, vol.5, pp.261-297, 2001. ,
DOI : 10.1051/ps:2001112
Stopped diffusion processes: boundary corrections and overshoot. Stochastic Process, Appl, vol.120, issue.2, pp.130-162, 2010. ,
DOI : 10.1016/j.spa.2009.09.014
URL : https://hal.archives-ouvertes.fr/hal-00157975
A survey and some generalizations of Bessel processes, Bernoulli, vol.9, issue.2, pp.313-349, 2003. ,
DOI : 10.3150/bj/1068128980
The probability distributions of the first hitting times of Bessel processes, Transactions of the American Mathematical Society, vol.365, issue.10, pp.5237-5257, 2013. ,
DOI : 10.1090/S0002-9947-2013-05799-6
The First-passage Time of the Brownian Motion to a Curved Boundary: an Algorithmic Approach, SIAM Journal on Scientific Computing, vol.38, issue.1, 2015. ,
DOI : 10.1137/151006172
URL : https://hal.archives-ouvertes.fr/hal-01110387
Efficient Estimation of One-Dimensional Diffusion First Passage Time Densities via Monte Carlo Simulation, Journal of Applied Probability, vol.21, issue.03, pp.699-712, 2011. ,
DOI : 10.1216/jiea/1181074930
Mathematical methods for financial markets, 2009. ,
DOI : 10.1007/978-1-84628-737-4
URL : https://hal.archives-ouvertes.fr/hal-00426898
On the comparison of Feller and Ornstein-Uhlenbeck models for neural activity, Biological Cybernetics, vol.105, issue.5, pp.457-465, 1995. ,
DOI : 10.1007/BF00201480
Boundary crossing of Brownian motion, Lecture Notes in Statistics, vol.40, 1986. ,
DOI : 10.1007/978-1-4615-6569-7
Markov chains, volume 2 of Cambridge Series in Statistical and Probabilistic Mathematics, 1999. ,
First exit time probability for multidimensional diffusions: A PDE-based approach, Journal of Computational and Applied Mathematics, vol.222, issue.1, pp.42-53, 2008. ,
DOI : 10.1016/j.cam.2007.10.043
Boundary crossing probability for Brownian motion, Journal of Applied Probability, vol.23, issue.01, pp.152-164, 2001. ,
DOI : 10.1111/1467-9965.00024
Continuous martingales and Brownian motion, 1999. ,
On an integral equation for first-passage-time probability densities, Journal of Applied Probability, vol.22, issue.02, pp.302-314, 1984. ,
DOI : 10.1016/0022-2496(80)90006-1
Stochastic Integrate and Fire Models: A Review on Mathematical Methods and Their Applications, Stochastic Biomathematical Models, pp.99-148, 2013. ,
DOI : 10.1007/978-3-642-32157-3_5
On evaluations and asymptotic approximations of first-passage-time probabilities, Advances in Applied Probability, vol.21, issue.01, pp.270-284, 1996. ,
DOI : 10.1016/0025-5564(83)90026-3
On hitting times of affine boundaries by reflecting Brownian motion and Bessel processes, Periodica Mathematica Hungarica, vol.28, issue.1, pp.75-101, 2011. ,
DOI : 10.1007/s10998-011-5075-2
URL : https://hal.archives-ouvertes.fr/hal-00657767
Bessel diffusions as a one-parameter family of diffusion processes, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.11, issue.1, pp.37-46, 1973. ,
DOI : 10.1007/BF00736006
Almost sure behavior of sums of independent random variables and martingales, Proc. Fifth Berkeley Sympos Contributions to Probability Theory, pp.315-343, 1965. ,
Crossing Probabilities for Diffusion Processes with Piecewise Continuous Boundaries, Methodology and Computing in Applied Probability, vol.45, issue.1, pp.21-40, 2007. ,
DOI : 10.1007/s11009-006-9002-6