An integral strong law of large numbers for processes with independent increments |
| |
Authors: | Howard G Tucker A Larry Wright |
| |
Institution: | (1) Department of Mathematics, University of California, 92717 Irvine, CA, USA;(2) Department of Mathematics, University of Arizona, 85721 Tucson, AZ, USA |
| |
Abstract: | For a stochastically continuous stochastic process with independent increments overD0,T], letN(t,ε) be the number of smaple function jumps that occur in the interval 0,t] of sizes less than −ε or greater than ε, where ε>0. LetM(t,ε)=EN(t,ε), and assumeM(t,0+)=∞ for 0<t≦T. If limε
↓0(M(t,ε)/M(T,ε)) exists and is positive for eacht∈(0,T], then limε
↓0(N(t,ε)/M(T,ε)) for allt∈(0,T] with probability one.
The research of Howard G. Tucker was supported in part by the National Science Foundation, Grant No. MCS76-03591A01. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|