Geometric Stable Laws Through Series Representations

Let (Xi ) be a sequence of i.i.d. random variables, and let N be a geometric random variable independent of (Xi ). Geometric stable distributions are weak limits of (normalized) geometric compounds, SN = X1 + · · · + XN , when the mean of N converges to infinity. By an appropriate representation of the individual summands in SN we obtain series representation of the limiting geometric stable distribution. In addition, we study the asymptotic behavior of the partial sum process SN (t) = ⅀( i=1 ... [N t] ) Xi , and derive series representations of the limiting geometric stable process and the corresponding stochastic integral. We also obtain strong invariance principles for stable and geometric stable laws.

Sums of a Random Number of Random Variables and their Approximations with ν- Accompanying Infinitely Divisible Laws

* Research supported by NATO GRANT CRG 900 798 and by Humboldt Award for U.S. Scientists.

On the Coherence Between Probability and Possibility Measures

* This paper is supported by CICYT (Spain) under Project TIN 2005-08943-C02-01.

Evaluating Misclassification Probability Using Empirical Risk

* The work is supported by RFBR, grant 04-01-00858-a

The B-Terminal Busy Probability Prediction

In the teletraffic engineering of all the telecommunication networks, parameters characterizing the terminal traffic are used. One of the most important of them is the probability of finding the called (B-terminal) busy. This parameter is studied in some of the first and last papers in Teletraffic Theory. We propose a solution in this topic in the case of (virtual) channel systems, such as PSTN and GSM. We propose a detailed conceptual traffic model and, based on it, an analytical macro-state model of the system in stationary state, with: Bernoulli– Poisson–Pascal input flow; repeated calls; limited number of homogeneous terminals; losses due to abandoned and interrupted dialling, blocked and interrupted switching, not available intent terminal, blocked and abandoned ringing and abandoned conversation. Proposed in this paper approach may help in determination of many network traffic characteristics at session level, in performance evaluation of the next generation mobile networks.

On the Extinction Probability for Bisexual Branching Processes in Varying Environments

2000 Mathematics Subject Classification: 60J80

Construction of Optimal Linear Codes by Geometric Puncturing

Dedicated to the memory of S.M. Dodunekov (1945–2012)Abstract. Geometric puncturing is a method to construct new codes. ACM Computing Classification System (1998): E.4.

Randomized Push-Out Mechanisms in Priority Queuing and their Probability Characteristics

2002 Mathematics Subject Classification: 60K25.

Sensitivity Analysis of Some Applied Probability Models

2000 Mathematics Subject Classi cation: Primary 90C31. Secondary 62C12, 62P05, 93C41.

Controlled Multitype Branching Models: Geometric Growth

2000 Mathematics Subject Classi cation: 60J80, 60F25.

On the Moving Boundary Hitting Probability for the Brownian Motion

2000 Mathematics Subject Classification: 60J65.

Upper and Lower Bounds for Ruin Probability

In this note we discuss upper and lower bound for the ruin probability in an insurance model with very heavy-tailed claims and interarrival times.

Extremes of Bivariate Geometric Variables with Application to Bisexual Branching Processes

2000 Mathematics Subject Classification: 60J80, 60G70.

An Estimate of the Probability Pr(X

2000 Mathematics Subject Classification: 33C90, 62E99

On the Recursive Estimation of the Location and of the Size of the Mode of a Probability Density

2000 Mathematics Subject Classification: 62G07, 62L20.