Introduction
In the study of the dynamics of a system subject to stochastic evolution, the attention is usually focused on the laws regulating the time course of the distribution function (df), or the transition probability density function (pdf), by which one can express the probability for the system to occupy at given times any preassigned configuration of the state space. In other words, it is customary to pay attention to the time evolution of the considered system through the state space starting either from a uniquely preassigned initial state or from a state whose probability distribution is assumed to be given.
Work partially supported by MIUR (PRIN 2008).
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References
Abrahams, J.: A survey of recent progress on level-crossing problems for random processes. In: Blake, I.F., Poor, H.V. (eds.) Communications and Networks - A Survey of Recent Advances, pp. 6–25. Springer, New York (1986)
Blake, I., Lindsey, W.: Level-Crossing Problems for Random Processes. IEEE Transactions Information Theory., IT 19, 295–315 (1973)
Buonocore, A., Nobile, A.G., Ricciardi, L.M.: A new integral equation for the evaluation of first-passage-time probability densities. Adv. Appl. Prob. 19, 784–800 (1987)
Buonocore, A., Caputo, L., Pirozzi, E., Ricciardi, L.M.: The First Passage Time Problem for Gauss-Diffusion Processes: Algorithmic Approaches and Applications to LIF Neuronal Model. Methodol. Comput. Appl. Probab. 13, 29–57 (2011)
Daniels, H.: The minimum of a stationary Markov process superimposed on a U-shaped trend. J. Appl. Prob. 6, 399–408 (1969)
Di Nardo, E., Nobile, A.G., Pirozzi, E., Ricciardi, L.M.: A computational approach to first-passage-time problems for Gauss-Markov processes. Adv. in Appl. Probab. 33(2), 453–482 (2001)
Jeanblanc, M., Rutkowski, M.: Modelling of default risk: an overview. In: Moderne Mathematical Finance: Theory and Practice, pp. 171–269. Higher Education Press, Beijing (2000)
Lo, C.F., Hui, C.H.: Computing the first passage time density of a time-dependent Ornstein-Uhlenbeck process to a moving boundary. Applied Mathematics Letters 19, 1399–1405 (2006)
Madec, Y., Japhet, C.: First passage time problem for drifted Ornstein-Uhlenbeck process. Math. Biosci. 189, 131–140 (2004)
Nobile, A.G., Ricciardi, L.M., Sacerdote, L.: Exponential trends of Ornstein-Uhlenbeck first-passage-time densities. J. Appl. Prob. 22, 360–369 (1985)
Redner, S.: A guide to First-Passage Processes. Cambridge University Press, Cambridge (2001), doi:10.2277/0521652480
Taillefumier, T., Magnasco, M.O.: A Fast Algorithm for the First-Passage Times of Gauss-Markov Processes with Hölder Continuous Boundaries. J. Stat. Phys. 140, 1130–1156 (2010)
Tuckwell, H.C.: Introduction to theoretical neurobiology (vol. 2): nonlinear and stochastic theories. Cambridge University Press, Cambridge (1998)
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Buonocore, A., Caputo, L., Pirozzi, E. (2012). First-Passage-Time for Gauss-Diffusion Processes via Integrated Analytical, Simulation and Numerical Methods. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2011. EUROCAST 2011. Lecture Notes in Computer Science, vol 6927. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27549-4_13
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