# Random-Time Isotropic Fractional Stable Fields

@article{Jung2011RandomTimeIF,
title={Random-Time Isotropic Fractional Stable Fields},
author={Paul Jung},
journal={Journal of Theoretical Probability},
year={2011},
volume={27},
pages={618-633}
}
• Paul Jung
• Published 20 December 2011
• Mathematics
• Journal of Theoretical Probability
Generalizing both Substable Fractional Stable Motions (FSMs) and Indicator FSMs, we introduce α-stabilized subordination, a procedure which produces new FSMs (H-self-similar, stationary increment symmetric α-stable processes) from old ones. We extend these processes to isotropic stable fields which have stationary increments in the strong sense, i.e., processes which are invariant under Euclidean rigid motions of the multi-dimensional time parameter. We also prove a Stable Central Limit Theorem…
2 Citations
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• 2015
Articles [1] H. Abdul-Rahman and N. Chernov. Fast and numerically stable circle fit.tic non-negative matrix factorization: Theory and application to microar-ray data analysis. [6] C. Fischbacher and

## References

SHOWING 1-10 OF 28 REFERENCES
Dilated Fractional Stable Motions
• Mathematics
• 2004
Dilated fractional stable motions are stable, self-similar, stationary increments random processes which are associated with dissipative flows. Self-similarity implies that their finite-dimensional
Indicator fractional stable motions
Using the framework of random walks in random scenery, Cohen and Samorodnitsky (2006) introduced a family of symmetric $\alpha$-stable motions called local time fractional stable motions. When
Decomposition of self-similar stable mixed moving averages
• Mathematics
• 2002
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
Stable stationary processes related to cyclic flows
• Mathematics
• 2004
We study stationary stable processes related to periodic and cyclic flows in the sense of Rosinski [Ann. Probab. 23 (1995) 1163–1187]. These processes are not ergodic. We provide their canonical
Stable mixed moving averages
• Mathematics
• 1993
SummaryThe class of (non-Gaussian) stable moving average processes is extended by introducing an appropriate joint randomization of the filter function and of the stable noise, leading to stable
Decomposition of stationary $\alpha$-stable random fields
It is shown that every stationary a-stable random field can be uniquely decomposed into the sum of three independent components belonging to these classes.
New classes of self-similar symmetric stable random fields
• Mathematics
• 1994
We construct two new classes of symmetric stable self-similar random fields with stationary increments, one of the moving average type, the other of the harmonizable type. The fields are defined
INTEGRAL-GEOMETRIC CONSTRUCTION OF SELF-SIMILAR STABLE PROCESSES
Recently, fractional Brownian motions are widely used to describe complex phenomena in several fields of natural science. In the terminology of probability theory the fractional Brownian motion is a
Structure of stationary stable processes
A connection between structural studies of stationary non-Gaussian stable processes and the ergodic theory of nonsingular flows is established and exploited. Using this connection, a unique
Fractional Brownian fields, duality, and martingales
• Mathematics
• 2006
In this paper the whole family of fractional Brownian motions is constructed as a single Gaussian field indexed by time and the Hurst index simultaneously. The field has a simple covariance structure