Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-27T23:52:01.121Z Has data issue: false hasContentIssue false
  • English
  • Français

Exit problem for a spectrally positive process

Published online by Cambridge University Press:  01 July 2016

D. J. Emery
D. J. Emery*
Affiliation:
The Polytechnic of Central London
Get access Rights & Permissions [Opens in a new window]

Abstract

The joint distributions of the exit time and exit value of a spectrally positive process, from semi-infinite and finite intervals, are derived in the form of Fourier-Laplace transforms. Also the probability that such a process makes its first exit from a finite interval via the lower end point is obtained explicitly.

Keywords

EXITINTERVALHOMOGENEOUS PROCESS WITH INDEPENDENT INCREMENTSWIENER-HOPFEXTENDED MARKOV PROPERTYPHRAGMÉN-LINDELÖF
Type
Research Article
Information
Advances in Applied Probability , Volume 5 , Issue 3 , December 1973 , pp. 498 - 520
Copyright
Copyright © Applied Probability Trust 1973 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Breiman, L. (1968) Probability. Addison-Wesley, Reading, Mass. Google Scholar
[2] Baxter, G. and Donsker, M. D. (1957) On the distribution of the supremum functional for processes with stationary independent increments. Trans. Amer. Math. Soc. 85, 73–87.CrossRefGoogle Scholar
[3] Gusak, D. V. (1969) On the joint distribution of the first exit time and exit value for homogeneous processes with independent increments. Theor. Probability Appl. 14, 14–23.Google Scholar
[4] Gusak, D. V. (1964) On the asymptotic distribution of the first exit time for a homogeneous process with independent increments. Ukrain. Mat. Z. 16, 4, 463–474.Google Scholar
[5] Gusak, D. V. and Korolyuk, V. S. (1968) On the first passage time across a given level for processes with independent increments. Theor. Probability Appl. 13, 448–456.Google Scholar
[6] Ito, K. and McKean, H. P. (1965) Diffusion Processes and their Sample Paths. Springer-Verlag, Berlin.Google Scholar
[7] Port, S. C. (1970) The exit distribution of an interval for completely asymmetric stable processes. Ann. Math. Statist. 41, 39–43.Google Scholar
[8] Port, S. C. and Stone, J. S. (1971) Infinitely divisible processes and their potential theory. Ann. Inst. Fourier 21, 2, 157–275.CrossRefGoogle Scholar
[9] Ray, D. (1958) Stable processes with an absorbing barrier. Trans. Amer. Math. Soc. 89, 16–24.Google Scholar
[10] Rogozin, B. A. (1966) On distributions of functionals related to boundary problems for processes with independent increments. Theor. Probability Appl. 11, 580–591.CrossRefGoogle Scholar
[11] Shtatland, E. S. (1965) On the distribution of the maximum of a process with independent increments. Theor. Probability Appl. 10, 483–487.Google Scholar
[12] Titchmarsh, E. C. (1939) The Theory of Functions. Clarendon Press, Oxford.Google Scholar
[13] Zolotarev, V. M. (1964) The first passage time of a level and the behaviour at infinity for a class of processes with independent increments. Theor. Probability Appl. 9, 653–662.Google Scholar