A weak convergence theorem for functionals of sums of independent random variables

Ken-ichi Yoshihara

Stochastic Processes and their Applications, 1982, vol. 12, issue 3, 293-299

Abstract: Let {[var epsilon]n1,...,[var epsilon]nn;n[greater-or-equal, slanted]1} be a sequence of series of random variables that are independently and identically distributed within each series. PutSn,i=[var epsilon]n1+...+[var epsilon]ni. We prove that under the conditions which assure the validity of the weak convergence of {Sn,[nt],0[less-than-or-equals, slant]t[less-than-or-equals, slant]1} to a process {X(t), 0[less-than-or-equals, slant]t[less-than-or-equals, slant]1} with stationary independent increments.

Date: 1982
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