A result on the first-passage time of an Ornstein-Uhlenbeck process

Statistics and Probability Letters

Volumn 77, Issue 18, 2007, Pages 1744-1749

  Ditlevsen, Susanne ^a  

^a UNIVERSITY OF COPENHAGEN   (Denmark)

Author keywords

Conditional moments; Eigenfunctions; Hermite polynomials; Laplace transform; Martingales

Indexed keywords

EID: 35548977214     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spl.2007.04.015     Document Type: Article

References (20)

1. Aalen O.O., and Gjessing H.K. Survival models based on the Ornstein-Uhlenbeck process. Lifetime Data Analysis 10 (2004) 407-423
2. Alili L., Patie P., and Pedersen J.L. Representations of the first hitting time density of an Ornstein-Uhlenbeck process. Stochastic Models 21 (2005) 967-980
3. Borodin A.N., and Salminen P. Handbook of Brownian motion-facts and formulae. Probability and its Applications (2002), Birkhauser, Basel
4. Bulsara A.R., Elston T.C., Doering C.R., Lowen S.B., and Lindberg K. Cooperative behavior in periodically driven noisy integrate-and-fire models of neuronal dynamics. Phys. Rev. E 53 (1996) 3958-3969
5. Cox J.C., Ingersoll J.E., and Ross S.A. A theory of the term structure of interest rates. Econometrica 53 (1985) 385-407
6. Ditlevsen S., and Lansky P. Estimation of the input parameters in the Ornstein-Uhlenbeck neuronal model. Phys. Rev. E 71 (2005) 011907
7. Ditlevsen S., and Lansky P. Estimation of the input parameters in the Feller neuronal model. Phys. Rev. E 73 (2006) 061910
8. Feller W. Diffusion processes in genetics. In: Neyman J. (Ed). Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability (1951), University of California Press, Berkeley 227-246
9. Jeanblanc M., and Rutkowski M. Modelling of default risk: an overview. Modern Mathematical Finance: Theory and Practice (2000), Higher Education Press, Beijing pp. 171-269
10. Karlin S., and Taylor H.M. A Second Course in Stochastic Processes (1981), Academic Press, New York
11. Kessler M., and Sørensen M. Estimating equations based on eigenfunctions for a discretely observed diffusion process. Bernoulli 5 2 (1999) 299-314
12. Lansky P., Sacerdote L., and Tomasetti F. On the comparison of Feller and Ornstein-Uhlenbeck models for neural activity. Biol. Cybernet. 73 (1995) 457-465
13. Lebedev N.N. Special Functions and Their Applications (1972), Dover, New York
14. Leblanc B., and Scaillet O. Path dependent options on yields in the affine term structure. Finance Stochastics 2 (1998) 349-367
15. Linetsky V. Computing hitting time densities for CIR and OU diffusions: applications to mean-reverting models. J. Comput. Finance 7 (2004) 1-22
16. Ricciardi L.M., and Sacerdote L. The Ornstein-Uhlenbeck process as a model of neuronal activity. Biol. Cybernet. 35 (1979) 1-9
17. Shimokawa T., Pakdaman K., Takahata T., Tanabe S., and Sato S. A first-passage-time analysis of the periodically forced noisy leaky integrate-and-fire model. Biol. Cybernet. 83 (2000) 327-340
18. Szegö G. Orthogonal Polynomials. fourth ed. (1975), American Mathematical Society, Providence, Rhode Island
19. Tuckwell H.C., Wan F.Y.M., and Rospars J.P. A spatial stochastic neuronal model with Ornstein-Uhlenbeck input current. Biol. Cybernet. 86 (2002) 137-145
20. Williams D. Probability with Martingales (1991), Cambridge University Press, Cambridge