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Limit laws for a stochastic process and random recursion arising in probabilistic modelling

Part of: Distribution theory - Probability Special processes Probability theory on algebraic and topological structures

Published online by Cambridge University Press:  01 July 2016

Svetlozar T. Rachev  and
Gennady Samorodnitsky
Svetlozar T. Rachev*
Affiliation:
University of California at Santa Barbara
Gennady Samorodnitsky*
Affiliation:
Cornell University
*
* Postal address: Department of Statistics and Applied Probability, University of California, Santa Barbara, CA 93106, USA.
** Postal address: School of ORIE, 206 ETC Building, Cornell University, Ithaca, NY 14853–3801, USA.
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Abstract

We study certain stochastic processes arising in probabilistic modelling. We discuss the limit behavior of these processes and estimate the rate of convergence to the limit.

Keywords

FINANCIAL MODELENVIRONMENTAL PROCESSESDISASTROUS EVENTLIMIT THEOREMLIMITING DISTRIBUTIONINFINITELY DIVISIBLE DISTRIBUTIONSTABLE DISTRIBUTIONGEOMETRIC STABLE DISTRIBUTIONRATE OF CONVERGENCE

MSC classification

Primary: 60E07: Infinitely divisible distributions; stable distributions
Secondary: 60B12: Limit theorems for vector-valued random variables (infinite-dimensional case) 60K30: Applications (congestion, allocation, storage, traffic, etc.)
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 27 , Issue 1 , March 1995 , pp. 185 - 202
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

Supported by NATO Scientific Affairs Division Grant CRG 900798 and Grant from UC Regents, University of California, Santa Barbara. S.T.R. also wishes to thank Econometric Institute, Erasmus University, Rotterdam for hospitality and support.

Supported by the ONR grant N00014-90-J-1287 and United States–Israel Binational Science Foundation.

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