Abstract
Let (B t + f(t))t∈[0,+∞) be a Brownian motion with polynomial drift f(t), where f(t) is a polynomial. Some Limit Results for Lower tail and large deviation probabilities estimates, and Level crossing probabilities estimates of (B t + f(t))t∈[0,+∞) are given in this paper.
Similar content being viewed by others
References
M. R. Leadbetter, G. Lindgren and H. Rootzen, Extremes and related Properties of random Sequences and processes, Springer-verlag, New York, 1983.
M. Ledoux, Isoperimetry and Gaussian Anaiysis, Lectures on probability theory and statistics, Lecture notes in math., 1648 (1996), 165–294, Springer-Verlag.
M. Ledoux and M. Talagrand, Probability on Banach spaces, Springer, Berlin, 1991.
W. V. Li and Q. M. Shao, Lower Tail probabilities of Gaussian processes, Annals of Probability, 32 (2004), 216–242.
M. Marcus and L. Shepp, Sample behavior of Gaussian processes. Proc. Sixth. Berkeleg Symp. Math. Stat. Prob., 2 (1972), 423–441, MR 53: 6710.
Olav Kallenberg, Foundations of modern probability. Springer-Verlaug, 2001.
J. Pickands, Asymptotic properties of maximum in a stationary Gaussian processes. Trans. Amer. Math. Soc., 145 (1969), 75–86.
D. Slepian, First passage time for a particular Gaussian process, Ann. Math. Stat., 32 (1961), 610–612.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Li, J. Some limit results for probabilities estimates of Brownian motion with polynomial drift. Indian J Pure Appl Math 41, 425–442 (2010). https://doi.org/10.1007/s13226-010-0026-9
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13226-010-0026-9