Random-Time Isotropic Fractional Stable Fields

Paul Jung ()
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Paul Jung: University of Alabama Birmingham

Journal of Theoretical Probability, 2014, vol. 27, issue 2, 618-633

Abstract: Abstract 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 which provides an intuitive picture of α-stabilized subordination. Finally we show that α-stabilized subordination of Linear FSMs produces null-conservative FSMs, a class of FSMs introduced by Samorodnitsky (Ann. Probab. 33(5):1782–1803, 2005).

Keywords: Fractional stable motion; Self-similar process; Stable field; 60G22; 60G52; 60G60 (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10959-012-0433-4

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