A REMARK ON THE ASYMPTOTIC BEHAVIOR OF SUBORDINATORS

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  • remark on the asymptotic behavior of subordinators

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紀要論文

Let X_1(t) and X_2(t) be independent subordinators and let X^<-1>2(t) be the right-continuous inverse of X_2. The asymptotic behavior of P[X_1(X^<-1>_2(t))≦x] as x→0+ for every fixed t>0 is studied. It is shown that the infinitesimal order is determined by the exponent of X_1 and the constant, which depends on t, is determined by the Levy measure of X_2. The problem is motivated by a generalized arc-sine law for one-dimensional diffusion processes.

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