Titlebook: Topics in Infinitely Divisible Distributions and Lévy Processes, Revised Edition; Alfonso Rocha-Arteaga,Ken-iti Sato Book 2019 Springer Na

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,Selfsimilar Additive Processes and Stationary Ornstein–Uhlenbeck Type Processes,ffect as some change of spatial scale. Under the condition of stochastic continuity and non-zero, the relation of the two scale changes is expressed by a positive number . called exponent. A Lévy process is selfsimilar if and only if it is strictly stable.

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Classes Lm and Their Characterization,Selfdecomposable distributions are extensions of stable distributions and form a subclass of the class of infinitely divisible distributions. In this chapter we will introduce, between the class .. of selfdecomposable distributions and the class . of stable distributions, a chain of subclasses called .., . = 1, …, .:

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,Classes , and Ornstein–Uhlenbeck Type Processes,stribution as . →., which is Gaussian. Processes of Ornstein–Uhlenbeck type are analogues of the Ornstein–Uhlenbeck process with the role of Brownian motion played by general Lévy processes. In this chapter we shall construct them, give the condition under which they have limit distributions, and st

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Book 2019ar additive processes and multivariate subordination. These topics are developed around a decreasing chain of classes of distributions .L.m., m = 0,1,...,∞, from the class .L.0. of selfdecomposable distributions to the class .L.∞. generated by stable distributions through convolution and convergence

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Inheritance in Multivariate Subordination,and examples. Section 5.2 discusses some generalization where the defining condition of selfdecomposability or stability for distributions on . involves a . × . matrix .. This is called operator generalization.

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