Limit Theorems for Regenerative Excursion Processes

This work is supported by Bulgarian NFSI, grant No. MM–704/97The regenerative excursion process Z(t), t = 0, 1, 2, . . . is constructed by two independent sequences X = {Xi , i ≥ 1} and Z = {Ti , (Zi (t), 0 ≤ t < Ti ), i ≥ 1}. For the embedded alternating renewal process, with interarrival times Xi – the time for the installation and Ti – the time for the work, are proved some limit theorems for the spent worktime and the residual worktime, when at least one of the means of Xi and Ti is infinite. Limit theorems for the process Z(t) are proved, too. Finally, some applications to the branching processes with state-dependent immigration are given

The Maximal Number of Particles in a Branching Process with State-Dependent Immigration

AMS subject classification: 60J80, 60J15.The limiting behavior of the maximal number of particles in the first n generations of a Bienaymé-Galton-Watson branching process with immigration in the state zero is studied

Extremes of Bivariate Geometric Variables with Application to Bisexual Branching Processes

2000 Mathematics Subject Classification: 60J80, 60G70.We obtain a limit theorem for the row maximum of a triangular array of bivariate geometric random vectors. An application of this limit theorem is provided for maximum family size within a generation of a bisexual branching process with varying geometric offspring laws.This paper is partly supported by NFSI-Bulgaria, Grant No. MM-1101/2001

The Vlachs in Macedonia in the 19th and 20th centuries

The article summarizes the known data about the localization and numerical distribution of various Vlach groups in Macedonia in the 19th and 20th centuries. Each Vlach group’s (Moscopolitan; Grammoustian; Farsherot and Moglenite Vlachs) migrations are analyzed separately, following them from their starting points from which they ventured forth and dispersed all over Ottoman Macedonia at the end of the 18th century, all the way to their dwellings in late 20th century in North Macedonia. In the second part of the article we review the thorough, yet unofficial statistics of Gustav Weigand and Vasil Kanchov about the number of Vlachs in Ottoman Macedonia, as well as the number and territorial distribution of the Vlachs in Macedonia, as shown in the 1921 census in the Kingdom of Serbs, Croats and Slovenes, the Yugoslav census from 1931, the six censuses conducted in socialist Yugoslavia in 1948, 1953, 1961, 1971, 1981 and 1991, and the two censuses in the Republic of Macedonia from 1994 and 2002.&nbsp;The article summarizes the known data about the localization and numerical distribution of various Vlach groups in Macedonia in the 19th and 20th centuries. Each Vlach group’s (Moscopolitan; Grammoustian; Farsherot and Moglenite Vlachs) migrations are analyzed separately, following them from their starting points from which they ventured forth and dispersed all over Ottoman Macedonia at the end of the 18th century, all the way to their dwellings in late 20th century in North Macedonia. In the second part of the article we review the thorough, yet unofficial statistics of Gustav Weigand and Vasil Kanchov about the number of Vlachs in Ottoman Macedonia, as well as the number and territorial distribution of the Vlachs in Macedonia, as shown in the 1921 census in the Kingdom of Serbs, Croats and Slovenes, the Yugoslav census from 1931, the six censuses conducted in socialist Yugoslavia in 1948, 1953, 1961, 1971, 1981 and 1991, and the two censuses in the Republic of Macedonia from 1994 and 2002

Making and keeping agreements in medieval Catalonia, 1000-1200

The author proposes an explanation of the diplomatic, judicial and political context in which the convenientia emerged -a documentary typology which establishes an individual and private agreement in Catalonia during the 11th and 12th centuries, concerning a wide variety of legal acts-, tracing a description of the development of the development of its political and social employment as an important element of structure. He also indicates the causes of its further declineL'autor proposa una explicació del context diplomàtic, jurídic i polític de l'aparició de la convenientia -una tipologia documental que estableix un contracte individual i privat al voltant d'una àmplia diversitat d'actes jurídics, a la Catalunya dels segles XI i XII. Estudia el desenvolupament del seu ús social i polític com un element important d'estructura i assenyala les causes de la seva decadènci

Option Pricing by Branching Process

2000 Mathematics Subject Classification: 60J80, 62P05.The randomly indexed Galton-Watson branching process has been used for the model of daily stock prices. Using this stock price process we derive a new formula for the price of European call options.This paper is partially supported by NSF of Bulgaria, Grant No VU-MI-105/2005

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

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