Operator-stable distributions and stable marginals

Stable Distributions

Stable Distributions

We give some explicit calculations for stable distributions and convergence to them, mainly based on less explicit results in Feller [3]. The main purpose is to provide ourselves with easy reference to explicit formulas and examples. (There are probably no new results.)

Operator geometric stable laws

Operator geometric stable laws are the weak limits of operator normed and centered geometric random sums of independent, identically distributed random vectors. They generalize operator stable laws and geometric stable laws. In this work we characterize operator geometric stable distributions, their divisibility and domains of attraction, and present their application to finance. Operator geome...

Lacunary series and stable distributions

By well known results of probability theory, any sequence of random variables with bounded second moments has a subsequence satisfying the central limit theorem and the law of the iterated logarithm in a randomized form. In this paper we give criteria for a sequence (Xn) of random variables to have a subsequence (Xnk) whose weighted partial sums, suitably normalized, converge weakly to a stable...

Tempered Stable Distributions and Processes

We investigate the class of tempered stable distributions and their associated processes. Our analysis of tempered stable distributions includes limit distributions, parameter estimation and the study of their densities. Regarding tempered stable processes, we deal with density transformations and compute their p-variation indices. Exponential stock models driven by tempered stable processes ar...