Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Physical Sciences and Mathematics
Convergence Rates For The Central Limit Theorem For Random Sums, Christopher E. Olson
Convergence Rates For The Central Limit Theorem For Random Sums, Christopher E. Olson
Mathematics & Statistics ETDs
Let (Xi} be a sequence of independent, identically-distributed random variables with EX2i < ꝏ and E(Xi - EXi)2 = 1.
Random Evolutions On Diffusion Processes, Donald Quiring
Random Evolutions On Diffusion Processes, Donald Quiring
Mathematics & Statistics ETDs
Let {V(t,ω), t ≥ O, ω ε Ω} be a diffusion process on the real line with infinitesimal operator 1/2σ2(⋅)D2 + m(⋅)D. Markov processes {Vn, n = 1,2,....} on the real line are constructed in such a way that the paths of Vn are step functions with jump size n-1/2 and
PO [lim sup |Vn(s)-V(s)| = 0] =1
n∞ 0≤s≤t,
where PO assigns probability one to paths starting at the origin at t = 0.
Let {TV(t), t≥0, vε R} be a family of linear contraction operators …