First Exit Times Through Curvilinear Boundaries for Stochastic Sequences

Let [Special characters omitted.] be a stochastic sequence and let [Special characters omitted.] be a predictable sequence. Define S(,n) for each n by S(,n) = X(,0) + X(,1)V(,1) + ... + V(,n)X(,n). Let [Special characters omitted.] be an increasing sequence of positive numbers and let [Special characters omitted.] Let 0 (LESSTHEQ) (alpha) (LESSTHEQ) 2 and let L be a positive Borel function. For each n, define W(,n) by W(,n) = (VBAR)V(,n)(VBAR)('(alpha))L(b(,n)/(VBAR)V(,n)(VBAR)) if V(,n) (NOT=) 0, W(,n) = 0 if V(,n) = 0. Under certain conditions on the b(,n)'s involving (alpha) and under certain conditions on the first two conditional truncated moments of the V(,n)X(,n)'s involving (alpha) and W(,n)'s we show there exist positive constants q(,0), c(,0), c(,1), and c(,2) such that [Special characters omitted.] for all (lamda) > 0. Furthermore, q(,0), c(,0), c(,1), and c(,2) do not depend on [Special characters omitted.] except through the conditions mentioned above.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Crabtree, James Claude

• Mathematics

Identifier

(UMI)AAI8502115

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/71223