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Moments of random sums and Robbins' problem of optimal stopping
Moments of random sums Robbins' problem Probability
2011/9/13
Abstract: Robbins' problem of optimal stopping asks one to minimise the expected {\it rank} of observation chosen by some nonanticipating stopping rule. We settle a conjecture regarding the {\it value...
Compositions, Random Sums and Continued Random Fractions of Poisson and Fractional Poisson Processes
Fractional birth process Bell polynomials Mittag–Leffler functions Fibonacci numbers continued fractions Poisson random fields
2011/9/8
Abstract: In this paper we consider the relation between random sums and compositions of different processes. In particular, for independent Poisson processes $N_\alpha(t)$, $N_\beta(t)$, $t>0$, we sh...
On the limit behaviour of random sums of independent random variables
the limit behaviour random sums independent random variables
2009/9/24
On the limit behaviour of random sums of independent random variables。
Weak convergence of random sums of infima of independent random variables
Weak convergence random sums independent random variables
2009/9/24
Weak convergence of random sums of infima of independent random variables。
RANDOM SUMS STOPPED BY A RARE EVENT:A NEW APPROXIMATION
Random sums limit theorems approximations reliability
2009/9/21
The convergence of a geometric sum of positive i.i.d.
random variables to an exponential distribution is a well-known re
sult. This convergence provided various and useful approximations in
reliabi...
Moderate Deviations for Random Sums of Heavy-Tailed Random Variables
large deviations moderate deviations extended regular variation Poisson process
2007/12/11
Let $\{X_n ; n\geq 1\}$ be a sequence of independent non-negative random variables with common distribution function $F$ having extended regularly varying tail and finite mean $\mu=E(X_1)$ and let $\{...