Summary
Let 0<h(ɛ)↑ and {S n} a renewal process. We find conditions under which ast→∞\(\sum\limits_{n \geqq \pi (t)} {h(S_n } ) \sim m^{ - 1} \int\limits_t^\infty {h(s)ds} \) wherem=ES 1, π(t) = min (n∶S n>t}. We apply these results to obtain sample path representation of local time at a point for a Markov process.
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Research supported in part by a grant from the National Science Foundation, USA
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Erickson, K.B. A limit theorem for renewal sequences with an application to local time. Z. Wahrscheinlichkeitstheorie verw Gebiete 57, 535–558 (1981). https://doi.org/10.1007/BF01025873
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DOI: https://doi.org/10.1007/BF01025873