Characterization of Stochastic Processes Determined Up to Shift

1976 ◽  
Vol 20 (3) ◽  
pp. 623-626 ◽  
Author(s):  
B. L. S. Prakasa Rao
Keyword(s):  
Stochastic Processes

SELF-SIMILARITY OF FREE STOCHASTIC PROCESSES

2006 ◽  
Vol 09 (03) ◽  
pp. 451-469 ◽  
Author(s):  
ZHAOZHI FAN
Keyword(s):  
Stochastic Processes ◽  
Self Similarity ◽  
Strict Stability ◽  
Classical Analogue ◽  
Self Similar

In this paper we study self-similarity of free stochastic processes. We establish the noncommutative counterpart of Lamperti's self-similar processes. We develop the characterization of noncommutative self-similar processes through a modification of Voiculescu transform, the free cumulant transform. We study the connection between free self-similarity, strict ⊞-stability and ⊞-self-decomposability. In particular, we derive the properties of free self-similar processes and their connection to strict ⊞-stability and ⊞-self-decomposability, that turn out to be consistent with their classical analogue.

Representation of Strongly Stationary Stochastic Processes

1993 ◽  
Vol 60 (3) ◽  
pp. 689-694 ◽  
Author(s):  
M. Di Paola
Keyword(s):  
Stochastic Process ◽  
Stochastic Processes ◽  
Linear Systems ◽  
Stationary Processes ◽  
Orthogonality Conditions ◽  
Probabilistic Characterization ◽  
Stationary Stochastic Processes ◽  
Fixed Order ◽  
Strongly Stationary

A generalization of the orthogonality conditions for a stochastic process to represent strongly stationary processes up to a fixed order is presented. The particular case of non-normal delta correlated processes, and the probabilistic characterization of linear systems subjected to strongly stationary stochastic processes are also discussed.

scholarly journals Extreme residual dependence for random vectors and processes

2011 ◽  
Vol 43 (01) ◽  
pp. 217-242 ◽  
Author(s):  
Laurens De Haan ◽  
Chen Zhou
Keyword(s):  
Stochastic Processes ◽  
Systemic Risk ◽  
Marginal Distribution ◽  
Banking System ◽  
Domain Of Attraction ◽  
Extreme Value Distribution ◽  
Distribution Functions ◽  
Two Dimensional ◽  
Higher Dimensional

A two-dimensional random vector in the domain of attraction of an extreme value distributionGis said to be asymptotically independent (i.e. in the tail) ifGis the product of its marginal distribution functions. Ledford and Tawn (1996) discussed a form of residual dependence in this case. In this paper we give a characterization of this phenomenon (see also Ramos and Ledford (2009)), and offer extensions to higher-dimensional spaces and stochastic processes. Systemic risk in the banking system is treated in a similar framework.

Characterization of stochastic processes by stochastic integrals

1983 ◽  
Vol 15 (1) ◽  
pp. 81-98 ◽  
Author(s):  
B. L. S. Prakasa Rao
Keyword(s):  
Stochastic Process ◽  
Stochastic Processes ◽  
Recent Work ◽  
Stochastic Integrals ◽  
Stable Processes ◽  
Process With Independent Increments ◽  
Independent Increments

Let be a continuous homogeneous stochastic process with independent increments. A review of the recent work on the characterization of Wiener and stable processes and connected results through stochastic integrals is presented. No proofs are given but appropriate references are mentioned.

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