A Note on First Passage Time Problems for Gaussian Processes and Varying Boundaries

IEEE Transactions on Information Theory

Volumn 29, Issue 3, 1983, Pages 454-457

  Ricciardi, Luigi M ^a   Sato, Shunsuke ^a  

^a OSAKA UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

PROBABILITY;

EID: 0020748101     PISSN: 00189448     EISSN: 15579654     Source Type: Journal    
DOI: 10.1109/TIT.1983.1056654     Document Type: Article

References (12)

1. L. M. Ricciardi, Diffusion Processes and Related Topics in Biology, Lecture Notes in Biomathematics, vol. 14. Berlin: Springer-Verlag, 1977.
2. I. F. Blake and W. C. Lindsey, “Level-crossing problems for random processes,” IEEE Trans. Inform. Theory, vol. IT-19, pp. 295-315, May 1973.
3. L. A. Shepp, “First passage time for a particular Gaussian process,” Ann. Math. Statist., vol. 42, pp. 946-951, 1971.
4. J. Durbin, “Boundary crossing probabilities for the Brownian motion and Poisson processes and techniques for computing the power of the Kolmogorov-Smirnov-test,” J. Appl. Prob., vol. 8, pp. 431-453, 1971.
5. C. S. Smith, “A note on boundary-crossing probabilities for the Brownian motion,” J. Appl. Prob., vol. 9, pp. 857-861, 1972.
6. K. S. Anderssen, F. R. De Hoog, and R. Weiss, “On the numerical solution Brownian motion processes,” J. Appl. Prob., vol. 10, pp. 409-418, 1973.
7. C. Park and S. R. Paranjape, “Probabilities of Wiener paths crossing differentiable curves,” Pac. J. Math., vol. 53, pp. 579-583, 1974.
8. C. Park and F. J. Schuurmann, “Evaluations of barrier-crossing probabilities of Wiener paths,” J. Appl. Prob., vol. 13, pp. 267-275, 1980.
9. A. I. Kostyukov, Yu. N. Ivanov and M. V. Kryzhanovsky, “Probability of neural spike initiation as a curve-crossing problem for Gaussian stochastic processes,” Bio. Cyber., vol. 39, pp. 157-163, 1981.
10. S. O. Rice, “The mathematical analysis of random noise,” Bell Syst. Tech. J., vol. 23, pp. 282-332, 1944; (in Selected Paper on Noise and Stochastic Processes, N. Wax, Ed. New York: Dover Publications, 1954).
11. M. S. Longuet-Higgins, “The distribution of intervals between zeros of a stationary random function,” Phil. Trans. Roy. Soc. London, vol. A254, pp. 557-599, 1962.
12. M. Kac, “On the distribution of values of trigonometric sums with linearly independent frequencies,” Amer. J. Math., vol. LXV, pp. 609-615, 1943.