Browsing by Author "Chen, X."
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Item Limiting behaviors for Brownian motion reflected on Brownian motion(Department of Mathematical Sciences, 2002) Chen, X.; Li, WenboSuppose that g(t) and Wt are independent Brownian motions starting from g(0) = W0 = 0. Consider the Brownian motion Yt re ected on g(t), obtained from Wt by the means of the Skorohod lemma. The upper and lower limiting behaviors of Yt are presented. The upper tail estimate on exit time is computed via principal eigenvalue.Item Quadratic Functionals and Small Ball Probabilities for the m-fold Brownian Motion(Department of Mathematical Sciences, 2002) Chen, X.; Li, WenboLet the Gaussian process Xm(t) be the m-fold integrated Brownian motion for positive integer m. The Laplace transform of the quadratic functional of Xm(t) is found by using an appropriate self-adjoint integral operator. The result is then used to show the power of a general connection between small ball probabilities for Gaussian process. The connection is discovered by introducing an independent random shift. Various interplay between our results and principal eigenvalues for non-uniform elliptic generators on an unbounded domain are discussed.