Almost Sure Limit Inferior for Increments of Stable Subordinators

Kokkada Vidyalaxmi, Korakote Nagaraj Ravi Prakash, Gooty Divanji^*

Department of Studies in Statistics, University of Mysore, Manasagangothri, Mysore, India.

DOI: 10.4236/oalib.1100812                

Abstract

Let {X(t), 0≤t<∞} be a sequence of completely asymmetric stable process or stable subordinators defined on a common probability space (Ω,ζ,P). In this paper, for proper selection of norming constants, we study almost sure limit inferior for increments of stable subordinators of geometrically increasing subsequences. Also we obtain similar results to delayed sums and study the existence of moments for boundary crossing random variables.

Keywords

Increments, Stable Subordinators, Law of Iterated Logarithm, Delayed Sums and Subsequences

Conflicts of Interest

The authors declare no conflicts of interest.

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