Abstract
In the paper, we develop methods for computing the distributions of special nonhomogeneous functionals of the Brownian motion. Some interesting examples of applications of these methods are considered. Bibliography: 7 titles.
Similar content being viewed by others
References
A. N. Kolmogorov, “Über die Analytischen Methoden in der Wahrscheinlichkeitsrechnung,” Math. Ann., 104, 415–458 (1931).
M. Kac, “On distribution of certain Wiener functionals,” Trans. Amer. Math. Soc., 65, No. 1, 1–13 (1949).
M. Kac, “On some connections between probability theory and differential and integral equations,” in: Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, Univ. of California Press, Berkeley and Los Angeles (1951), pp. 189–215.
R. Z. Khas’minskii, “Probability distribution of functionals of trajectories of a random process of diffusion type,” Dokl. Akad. Nauk SSSR, 104, No. 1, 22–25 (1955).
A. N. Borodin and I. A. Ibragimov, “Limit theorems for functionals of random walks,” Proc. Steklov Inst. Math., No. 2 (1995).
A. N. Borodin, “On the distribution of functionals of Brownian motion stopped at the moment inverse to an occupation time,” Zap. Nauchn. Semin. POMI, 228, 39–56 (1996).
A. N. Borodin and P. Salminen, Handbook of Brownian Motion — Facts and Formulae, 2nd edition, Birkhäuser-Verlag, Basel (2002).
Author information
Authors and Affiliations
Additional information
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 320, 2004, pp. 5–29.
Rights and permissions
About this article
Cite this article
Borodin, A.N. Distribution of special nonhomogeneous functionals. J Math Sci 137, 4487–4501 (2006). https://doi.org/10.1007/s10958-006-0241-4
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10958-006-0241-4