For the renewal counting process M(t)=min{k:Skt} and the independent of it nonnegative random variable T, we investigate the asymptotic behaviour of P(M(t)T) and P(M(t)=K(t)x|M(t)T) in cases when the interarrival times have an infinite mean. These quantities appear in a natural way when...

Limiting distributions for the spent and residual life times in a superposition of independent renewal processes are obtained in the case when the interarrival times belong to domains of attraction of stable laws.

We obtain limit theorems for the row extrema of a triangular array of zero-modified geometric random variables. Some of this is used to obtain limit theorems for the maximum family size within a generation of a simple branching process with varying geometric offspring laws.

This paper examines the pricing of barrier options when the price of the underlying asset is modeled by a branching process in a random environment (BPRE). We derive an analytical formula for the price of an up-and-out call option, one form of a barrier option. Calibration of the model...

This paper examines the pricing of barrier options when the price of the underlying asset is modeled by a branching process in a random environment (BPRE). We derive an analytical formula for the price of an up-and-out call option, one form of a barrier option. Calibration of the model...

It is hard to find explicit expressions for the renewal function U(x)=∑n=0∞F∗n(x). Many researchers have made attempts to find suitable approximations for U(x). In this paper we present simple approximations and show that they cover many of the known results.

The point process defines the sequence of maxima . Using time and space scaling it is possible to define different sequences of random time changed extremal processes. The convergence of such sequences to nondegenerate extremal processes is proved in case where the time and space components of...

Abstract We propose modeling COVID-19 infection dynamics using a class of two-type branching processes. These models require only observations on daily statistics to estimate the average number of secondary infections caused by a host and to predict the mean number of the non-observed infected...