35 research outputs found
Large deviations for random walks under subexponentiality: the big-jump domain
For a given one-dimensional random walk with a subexponential
step-size distribution, we present a unifying theory to study the sequences
for which as
uniformly for . We also investigate the stronger "local"
analogue, . Our
theory is self-contained and fits well within classical results on domains of
(partial) attraction and local limit theory. When specialized to the most
important subclasses of subexponential distributions that have been studied in
the literature, we reproduce known theorems and we supplement them with new
results.Comment: Published in at http://dx.doi.org/10.1214/07-AOP382 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Counting cliques and cycles in scale-free inhomogeneous random graphs
Scale-free networks contain many small cliques and cycles. We model such
networks as inhomogeneous random graphs with regularly varying
infinite-variance weights. For these models, the number of cliques and cycles
have exact integral expressions amenable to asymptotic analysis. We obtain
various asymptotic descriptions for how the average number of cliques and
cycles, of any size, grow with the network size. For the cycle asymptotics we
invoke the theory of circulant matrices
Arbitrarily Accurate Approximation of Numerical Characteristics of Stationary ALOHA Channels
Lower bound for average delay in unblocked random access algorithm with orthogonal preambles
Estimates for interval probabilities of the sums of random variables with locally subexponential distributions
An alternating risk reserve process - part I
We consider an alternating risk reserve process with a threshold dividend strategy. The process can be in two different states and the state of the process can only change just after claim arrival instants. If at such an instant the capital is below the threshold, the system is set to state 1 (paying no dividend), and if the capital is above the threshold, the system is set to state 2 (paying dividend). Our interest is in the survival probabilities. In the case of exponentially distributed claim sizes, survival probabilities are found by solving a system of integro-differential equations. In the case of generally distributed claim sizes, they are expressed in the survival probabilities of the corresponding standard risk reserve processes