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

Branching Stochastic Processes: Regulation, Regeneration, Estimation, Applications

2000 Mathematics Subject Classification: 60J80.This is a survey of the works of Bulgarian mathematicians in the area of Branching Stochastic Processes

Nonlinear Normalization in Limit Theorems for Extremes

2000 Mathematics Subject Classification: 60G70, 60F05.It is well known that under linear normalization the maxima of iid random variables converges in distribution to one of the three types of max-stable laws: Frechet, Gumbel and Weibull. During the last two decades the first author and her collaborators worked out a limit theory for extremes and extremal processes under non-linear but monotone normalizing mappings. In this model there is only one type of max-stable distributions and all continuous and strictly increasing df's belong to it. In a recent paper on General max-stable laws, Sreehari points out two "confusing" results in Pancheva (1984). They concern the explicit form of a max-stable df with respect to a continuous one-parameter group of max-automorphisms, and domain of attraction conditions. In the present paper the first claim is answered by a detailed explanation of the explicit form, while for the second we give a revised proof. The rate of convergence is also discussed

Total Progeny in a Subcritical Branching Process with two Types of Immigration

2000 Mathematics Subject Classification: 60J80, 60F05We consider subcritical Bellman-Harris branching processes with two types of immigration - one appears whenever the process hits zero state and an other one is in accordance of an independent renewal process. The law of large numbers (LLN) for the total progeny of these processes and Anscombe's type central limit theorem (CLT) for the total number of particles in the cycles completely finished by the moment t are obtained.The paper is supported by NFSI-Bulgaria, Grant No. MM-1101/2001

NNLO corrections to top-pair production at hadron colliders: the all-fermionic scattering channels

This is a second paper in our ongoing calculation of the next-to-next-to-leading order (NNLO) QCD correction to the total inclusive top-pair production cross-section at hadron colliders. In this paper we calculate the reaction $q\bar q \to t\bar t + q\bar q$ which was not considered in our previous work on $q\bar q \to t\bar t +X$ due to its phenomenologically negligible size. We also calculate all remaining fermion-pair-initiated partonic channels $qq', q\bar q'$ and $qq$ that contribute to top-pair production starting from NNLO. The contributions of these reactions to the total cross-section for top-pair production at the Tevatron and LHC are small, at the permil level. The most interesting feature of these reactions is their characteristic logarithmic rise in the high energy limit. We compute the constant term in the leading power behavior in this limit, and achieve precision that is an order of magnitude better than the precision of a recent theoretical prediction for this constant. All four partonic reactions computed in this paper are included in our numerical program Top++. The calculation of the NNLO corrections to the two remaining partonic reactions, $qg\to t\bar t+X$ and $gg\to t\bar t+X$, is ongoing.Comment: 1+16 pages; 3 figure

Bottom-quark fragmentation: comparing results from tuned event generators and resummed calculations

We study bottom-quark fragmentation in e+e- annihilation, top and Higgs decay H -> b bbar, using Monte Carlo event generators, as well as calculations, based on the formalism of perturbative fragmentation functions, which resum soft- and collinear-radiation effects in the next-to-leading logarithmic approximation. We consider the PYTHIA and HERWIG generators, and implement matrix-element corrections to the parton shower simulation of the H -> b bbar process in HERWIG. We tune the Kartvelishvili, string and cluster models to B-hadron data from LEP and SLD, and present results in both x_B and moment spaces. The B-hadron spectra yielded by HERWIG, PYTHIA and resummed calculations show small discrepancies, which are due to the different approaches and models employed and to the quality of the fits to the e+e- data.Comment: 22 pages, 11 colour figures. Minor changes in the text, published versio

On the renormalization of multiparton webs

We consider the recently developed diagrammatic approach to soft-gluon exponentiation in multiparton scattering amplitudes, where the exponent is written as a sum of webs - closed sets of diagrams whose colour and kinematic parts are entangled via mixing matrices. A complementary approach to exponentiation is based on the multiplicative renormalizability of intersecting Wilson lines, and their subsequent finite anomalous dimension. Relating this framework to that of webs, we derive renormalization constraints expressing all multiple poles of any given web in terms of lower-order webs. We examine these constraints explicitly up to four loops, and find that they are realised through the action of the web mixing matrices in conjunction with the fact that multiple pole terms in each diagram reduce to sums of products of lower-loop integrals. Relevant singularities of multi-eikonal amplitudes up to three loops are calculated in dimensional regularization using an exponential infrared regulator. Finally, we formulate a new conjecture for web mixing matrices, involving a weighted sum over column entries. Our results form an important step in understanding non-Abelian exponentiation in multiparton amplitudes, and pave the way for higher-loop computations of the soft anomalous dimension.Comment: 60 pages, 15 figure