A weak convergence theorem for functionals of sums of independent random variables
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.
Year of publication: |
1982
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Authors: | Yoshihara, Ken-ichi |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 12.1982, 3, p. 293-299
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Publisher: |
Elsevier |
Saved in:
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