Abstract The decoy-state method substantially improves the performance of quantum key distribution (QKD) and perfectly solves crucial issues caused by multiphoton pulses. In recent years, has occupied a position in practicality, almost all QKD systems have employed method. However, imperfections traditional intensity modulators limit bring side channels. this work, special modulator its accompa...

Univariate stable distributions arose within the context of the central limit theorem as limit laws for sums of i.i.d. random variables. Except for the gaussian laws, all the stable distributions are heavy-tailed. This explains why stable distribution models are very attractive for statisticians. The fact that stable laws are limiting says a lot about possible genesis of the corresponding rando...

Stable distributions are a class of probability distributions that allow heavy tails and skewness. In addition to theoretical reasons for using stable laws, they are a rich family that can accurately model different kinds of financial data. We review the basic facts, describe programs that make it practical to use stable distributions, and give examples of these distributions in finance. A non-...

It is known that each symmetric stable distribution in Rd is related to a norm on Rd that makes Rd embeddable in Lp([0, 1]). In case of a multivariate Cauchy distribution the unit ball in this norm corresponds is the polar set to a convex set in Rd called a zonoid. This work exploits most recent advances in convex geometry in order to come up with new probabilistic results for multivariate stab...

Financial returns exhibit common behavior described at best by factor models, but also fat tails, which may be captured by α-stable distributions. This paper concentrates on estimating factor models with multivariate α-stable distributed and independent factors and idiosyncratic noises under the assumption of time constant distribution (static factor models) or time-varying conditional distribu...