# MINIMAL INTEGRAL REPRESENTATIONS OF STABLE PROCESSES

@inproceedings{Rosnski1998MINIMALIR, title={MINIMAL INTEGRAL REPRESENTATIONS OF STABLE PROCESSES}, author={Jan Ros{\'i}nski}, year={1998} }

Abstract: Minimal integral representations are defined for general st ochastic processes and completely characterized for stable processes ( symmetric and asymmetric). In the stable case, minimal representations are described b y rigid subsets of theLspaces which are investigated here in detail. Exploiting th is relationship, various tests for the minimality of representations of stable processes a r obtained and used to verify this property for many representations of processes of inte res .

## 18 Citations

Minimality, Rigidity, and Flows

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- 2017

A symmetric stable random process has many integral representations. Among these, the so-called minimal representations play a fundamental role, as described in the chapter. Minimal representations…

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Decomposability for stable processes

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We characterize all possible independent symmetric α-stable (SαS) components of an SαS process, 0<α<2. In particular, we focus on stationary SαS processes and their independent stationary SαS…

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Stable non-Gaussian self-similar mixed moving averages can be decomposed into several components. Two of these are the periodic and cyclic fractional stable motions which are the subject of this…

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Abstract. Let α? (1,2) and Xα be a symmetric α-stable (S α S) process with stationary increments given by the mixed moving average
where is a standard Lebesgue space, is some measurable function…

Can continuous-time stationary stable processes have discrete linear representations?

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Two integrable random vectors ξ and ξ* in IRd are said to be zonoid equivalent if, for each u∈IRd, the scalar products 〈ξ,u〉 and 〈ξ*,u〉 have the same first absolute moments. The paper analyses…

Maharam extension and stationary stable processes

- Mathematics
- 2012

We give a second look at stationary stable processes by interpreting the self-similar property at the level of the Levy measure as characteristic of a Maharam system. This allows us to derive…

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Self-similar stable mixed moving average processes can be related to nonsingular flows through their minimal representations. Self-similar stable mixed moving averages related to dissipative flows…

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