No CrossRef data available.
Article contents
Approximation to the exit probability of a continuous Gaussian process over a U-shaped boundary of increasing curvature
Part of:
Markov processes
Published online by Cambridge University Press: 14 July 2016
Abstract
A simple approximation to the probability of crossing a U-shaped boundary by a Brownian motion is given. The larger the second derivative of the curve at a minimum point, the higher the accuracy of the approximation. The result is also extended to a class of continuous Gaussian processes with definite properties. Numerical examples are given.
MSC classification
Primary:
60J65: Brownian motion
- Type
- Research Papers
- Information
- Copyright
- Copyright © Applied Probability Trust 1995
References
[1]
Balabushkin, A. N. (1991) Forecasting of the state of a dynamic object at the time of reaching the boundary under small perturbations. Automation and Remote Control
52, 1533–1538.Google Scholar
[2]
Balabushkin, A. N. and Gul'Ko, F. B. (1988) Prediction of extremal values of phase variables of stochastic systems. Automation and Remote Control
49, 743–748.Google Scholar
[3]
Durbin, J. (1985) The first-passage density of a continuous Gaussian process to a general boundary. J. Appl. Prob.
22, 99–122.Google Scholar
[4]
Durbin, J. (1992) The first-passage density of the Brownian motion process to a curved boundary. J. Appl. Prob.
29, 291–304.Google Scholar
[5]
Ferebee, B. (1982) The tangent approximation to one-sided Brownian exit densities. Z. Wahrscheinlichkeitsth.
61, 309–326.Google Scholar
[6]
Ferebee, B. (1983) An asymptotic expansion for one-sided Brownian exit densities. Z. Wahrscheinlichkeitsth.
63, 1–15.Google Scholar
[7]
Fernique, X. (1975) Regularité des Trajectoires des Fonctions Aléatoires Gaussiennes.
Lecture Notes in Mathematics 480, Springer-Verlag, Berlin.Google Scholar
[8]
Jennen, C. and Lerche, H. R. (1981) First-exit densities of Brownian motion through one-sided moving boundaries. Z. Wahrscheinlichkeitsth.
55, 133–148.Google Scholar
[9]
Slepian, D. (1962) The one-sided barrier problem for Gaussian noise. Bell System Tech. J.
41, 463–501.Google Scholar