Subcritical Randomly Indexed Branching Processes

2000 Mathematics Subject Classification: 60J80, 62P05.The paper continues the study of the randomly indexed branching processes in the subcritical case. The asymptotic behavior of the moments and the probability for non-extinction is investigated. Conditional limiting distributions are obtained.The first author wish to thank the Organizing Committee of the ISCPS, SDA, and WBPA 2010 for the financial support which allows him to participate in the conference

An Estimate of the Probability Pr(X<Y)

2000 Mathematics Subject Classification: 33C90, 62E99In the area of stress-strength models there has been a large amount of work as regards estimation of the probability R = Pr(X<Y) when X and Y are independent random variables belonging to the same univariate family of distributions. In this paper we propose an estimate of this quantity based on a simple property of the uniform distribution. We illustrate the use of the estimate with bootstrap confidence intervals for four commonly known distributions (normal, exponential, gamma and beta).The third author is supported by by NFSI-Bulgaria, Grant No. MM-1101/2001

Resummation of small-x double logarithms in QCD: semi-inclusive electron-positron annihilation

We have derived the coefficients of the highest three 1/x-enhanced small-x logarithms of all timelike splitting functions and the coefficient functions for the transverse fragmentation function in one-particle inclusive e^+e^- annihilation at (in principle) all orders in massless perturbative QCD. For the longitudinal fragmentation function we present the respective two highest contributions. These results have been obtained from KLN-related decompositions of the unfactorized fragmentation functions in dimensional regularization and their structure imposed by the mass-factorization theorem. The resummation is found to completely remove the huge small-x spikes present in the fixed-order results for all quantities above, allowing for stable results down to very small values of the momentum fraction and scaling variable x. Our calculations can be extended to (at least) the corresponding as^n ln^(2n-l) x contributions to the above quantities and their counterparts in deep-inelastic scattering.Comment: 27 pages, LaTeX, 6 eps-figure

On the number of renewals in random time

For the renewal counting process M(t)=min{k:Sk>t} and the independent of it nonnegative random variable T, we investigate the asymptotic behaviour of P(M(t)

BARRIER OPTION PRICING BY BRANCHING PROCESSES

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 parameters is performed using market prices of standard call options. Our results show that the prices of barrier options that are priced with the BPRE model deviate significantly from those modeled assuming a lognormal process, despite the fact that for standard options, the corresponding differences between the two models are relatively small.Barrier option, up-and-out call option, Bienayme-Galton-Watson branching process, branching process in a random environment

The International Linear Collider: Report to Snowmass 2021

The International Linear Collider (ILC) is on the table now as a new global energy-frontier accelerator laboratory taking data in the 2030s. The ILC addresses key questions for our current understanding of particle physics. It is based on a proven accelerator technology. Its experiments will challenge the Standard Model of particle physics and will provide a new window to look beyond it. This document brings the story of the ILC up to date, emphasizing its strong physics motivation, its readiness for construction, and the opportunity it presents to the US and the global particle physics community