Self-Similarity and Lamperti Transformation for Random Fields

In this paper we study the α-stable continuous-state branching processes (for α ∈ (1, 2]) and the α-stable continuous-state branching processes conditioned never to become extinct in the light of positive self-similarity. Understanding the interaction of the Lamperti transformation for continuous-state branching processes and the Lamperti transformation for positive, self-similar Markov processes gives access to a number of explicit results concerning the paths of α-stable continuous-state branching processes and α-stable continuous-state branching processes conditioned never to become extinct.

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Self-similarity of Brownian motion and a large deviation principle for random fields on a binary tree

Probability Theory and Related Fields ◽

10.1007/bf01311346 ◽

1994 ◽

Vol 98 (1) ◽

pp. 7-20 ◽

Cited By ~ 3

Author(s):

Nina Gantert

Keyword(s):

Brownian Motion ◽

Random Fields ◽

Binary Tree ◽

Large Deviation Principle ◽

Large Deviation ◽

Self Similarity ◽

Deviation Principle

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From Stationarity to Self-similarity, and Back: Variations on the Lamperti Transformation

Processes with Long-Range Correlations - Lecture Notes in Physics ◽

10.1007/3-540-44832-2_5 ◽

2003 ◽

pp. 88-117 ◽

Cited By ~ 14

Author(s):

Patrick Flandrin ◽

Pierre Borgnat ◽

Pierre-Olivier Amblard

Keyword(s):

Self Similarity ◽

Lamperti Transformation

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Self-similarity based action recognition using Conditional Random Fields

2012 International Conference on Information Retrieval & Knowledge Management ◽

10.1109/infrkm.2012.6204984 ◽

2012 ◽

Cited By ~ 1

Author(s):

Imran N. Junejo

Keyword(s):

Action Recognition ◽

Random Fields ◽

Conditional Random Fields ◽

Self Similarity

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Continuous-State Branching Processes and Self-Similarity

Journal of Applied Probability ◽

10.1239/jap/1231340239 ◽

2008 ◽

Vol 45 (4) ◽

pp. 1140-1160 ◽

Cited By ~ 6

Author(s):

A. E. Kyprianou ◽

J. C. Pardo

Keyword(s):

Markov Processes ◽

Branching Processes ◽

Self Similarity ◽

Lamperti Transformation ◽

Continuous State ◽

Self Similar

In this paper we study the α-stable continuous-state branching processes (for α ∈ (1, 2]) and the α-stable continuous-state branching processes conditioned never to become extinct in the light of positive self-similarity. Understanding the interaction of the Lamperti transformation for continuous-state branching processes and the Lamperti transformation for positive, self-similar Markov processes gives access to a number of explicit results concerning the paths of α-stable continuous-state branching processes and α-stable continuous-state branching processes conditioned never to become extinct.

Download Full-text