On lower limits and equivalences for distribution tails of randomly stopped sums
Copyright policy )On lower limits and equivalences for distribution tails of randomly stopped sums
For a distribution $F^{*τ}$ of a random sum $S_τ=ξ_1+...+ξ_τ$ of i.i.d. random variables with a common distribution $F$ on the half-line $[0,\infty)$, we study the limits of the ratios of tails $\bar{F^{*τ}}(x)/\bar{F}(x)$ as $x\to\infty$ (here, $τ$ is a counting random variable which does not depend on $\{ξ_n\}_{n\ge1}$). We also consider applications of the results obtained to random walks, compound Poisson distributions, infinitely divisible laws, and subcritical branching processes.
Published in at http://dx.doi.org/10.3150/07-BEJ111 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)
- Technical University Eindhoven Netherlands
- University of Manchester United Kingdom
- University of Manchester United Kingdom
- Novosibirsk State University Russian Federation
- Sobolev Institute of Mathematics Russian Federation
Stopping times; optimal stopping problems; gambling theory, Probability (math.PR), convolution tail, lower limit, Convolution tail, Lower limit, Subexponential distribution, Convolution equivalence, FOS: Mathematics, convolution equivalence, QA, Randomly stopped sums, subexponential distribution, Mathematics - Probability, randomly stopped sums
Stopping times; optimal stopping problems; gambling theory, Probability (math.PR), convolution tail, lower limit, Convolution tail, Lower limit, Subexponential distribution, Convolution equivalence, FOS: Mathematics, convolution equivalence, QA, Randomly stopped sums, subexponential distribution, Mathematics - Probability, randomly stopped sums
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