arXiv subjects
Publications and source records attributed to Lev B. Klebanov.
In the present paper, we discuss contra-arguments concerning the use of Pareto-Levý distributions for modeling in Finance. It appears that such probability laws do not provide sufficient number of outliers observed in real data. Connection with the classical limit theorem for heavy-tailed distributions with such type of models is also questionable. The idea of alternative modeling is given.
We give a necessary and sufficient condition for symmetric infinitely divisible distribution to have Gaussian component. The result can be applied to approximation the distribution of finite sums of random variables. Particularly, it shows that for a large class of distributions with finite variance stable approximation appears to be better than Gaussian. keywords: infinitely divisible distributions; Gaussian component; approximations of sums of random variables.
A generalization of stable and casual stable probability distribution is proposed. The notion of $\go G$-casual stability can be used to introduce discrete analogues of stable distributions on the sent $\mathbb Z$ of integers. In contrary to limit definition of stable distributions on $\mathbb Z$ our has algebraic character. Examples of corresponding limit theorems are given. Keywords: stable distributions; casual stable distribution; discrete stable distributions; limit theorems
We construct an autoregressive model with random coefficients that has a stationary distribution after proper normalization. This limit distribution is found to be stable.
Since the turn of the century, there has been increased interest in the application of heavy-tailed distributions, particularly stable distributions, to problems in physics and finance. Although, the tails of stable distributions provide a better fit to real-world data, they are too fat to describe empirical distributions. To remedy this drawback of stable distributions, so-called tempered variants of stable distributions have been proposed. In this paper, we argue that the tempering should be connected to the model leading to heavy tailed distribution and propose several tempering procedures in connection with corresponding models
A new class of probability distributions closely connected to generalized hyperbolic distributions is introduced. It is more adapted to study the distributions of sums of random number of random variables. The properties of these distributions are studied. It seems, that this class may be useful for asset returns modeling.
This article deals with different generalizations of the discrete stability property. Three possible definitions of discrete stability are introduced, followed by a study of some particular cases of discrete stable distributions and their properties.
Self-similarity of systems is very popular and intensively developing field during last decades. To this field belong so-called stable distributions and their generalization. In Klebanov and Slámová (2014) there was given an approach to define additive systems with the property of random self-similarity - casual stability (c.s.). Here we continue study the notion of casual stability for additive systems of random variables (r.v.). We also give a modification of this definition and spread them on multiplicative systems of r.v. and on the system with operations of taking minimum or maximum of r.v. The case of systems with a random number of elements is also considered.
Here we introduce some new classes of discrete stable random variables, which are useful for understanding of a new general notion of stability of random variables called us as casual stability. There are given some examples of casual and discrete stable random variables. We also propose a class of discrete stable random variables for a description of rating of scientific work.
In some fields of applications of stable distributions, especially in economics, it appears, that data have distributions similar to stable in a large region, but do not have such heavy tails. Our aim in this note is to propose several methods of approximation of stable distributions by some discrete distributions, which may have different tail behavior. In a sense the introduced distributions form an alternative to tempered stable distributions that combine Gaussian and stable behavior.
We introduce a class of distributions originating from an exponential family and having a property related to the strict stability property. A characteristic function representation for this family is obtained and its properties are investigated. The proposed class relates to stable distributions and includes Inverse Gaussian distribution and Levy distribution as special cases. Due to its origin, the proposed distribution has a sufficient statistic. Besides, it combines stability property at lower scales with an exponential decay of the distribution's tail and has an additional flexibility due to the convenient parametrization. Apart from the basic model, certain generalizations are considered, including the one related to geometric stable distributions.