Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-13T06:58:21.835Z Has data issue: false hasContentIssue false
  • English
  • Français

On the first hitting place of the integrated Wiener process

Published online by Cambridge University Press:  01 July 2016

Mario Lefebvre  and
Éric Léonard
Mario Lefebvre
Affiliation:
École Polytechnique de Montréal
Éric Léonard*
Affiliation:
École Polytechnique de Montréal
*
∗Postal address for both authors: Département de mathématiques appliquées, École Polytechnique de Montréal, Case postale 6079, Succursale “A”, Montréal, Québec, Canada H3C 3A7.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let dx(t) = y(t) dt, where y(t) is a one-dimensional Wiener process. In this note, we obtain a formula for the moment-generating function of y(T), where T is the 1/2-winding time about the origin of the integrated Wiener process x(t).

Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 21 , Issue 4 , December 1989 , pp. 945 - 948
Copyright
Copyright © Applied Probability Trust 1989 

Footnotes

Research supported by the Natural Sciences and Engineering Research Council of Canada.

References

Abramowitz, M. and Stegun, I. A. (1972) Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Wiley, New York.Google Scholar
Goldman, M. (1971) On the first passage of the integrated Wiener process. Ann. Math. Statist. 42, 2150–2155.Google Scholar
Gor'Kov, Ju. P. (1975) A formula for the solution of a boundary value problem for the stationary equation of Brownian motion. Soviet Math. Dokl. 16, 904–908.Google Scholar
Gradshteyn, I. S. and Ryzhik, I. M. (1980) Tables of Integrals, Series and Products. Academic Press, New York.Google Scholar
Lefebvre, M. (1989) First-passage densities of a two-dimensional process. SIAM J. Appl. Math. 49.Google Scholar
Mckean, H. P. Jr. (1963) A winding problem for a resonator driven by a white noise. J. Math. Kyoto Univ. 2, 227–235.Google Scholar