Operator-semistable,operator semi-selfdecomposable probability measures and related nested classes on <Emphasis Type="Italic">p</Emphasis>-adic vector spaces |
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Authors: | Makoto Maejima Riddhi Shah |
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Institution: | (1) Keio University, Yokohama, Japan;(2) School of Mathematics, TIFR, Mumbai, India |
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Abstract: | Let V be a finite dimensional p-adic vector space and let τ be an operator in GL(V). A probability measure μ on V is called τ-decomposable or
if μ = τ(μ)* ρ for some probability measure ρ on V. Moreover, when τ is contracting, if ρ is infinitely divisible, so is μ, and if ρ is embeddable, so is μ. These two subclasses
of
are denoted by L
0(τ) and L
0
#(τ) respectively. When μ is infinitely divisible τ-decomposable for a contracting τ and has no idempotent factors, then it
is τ-semi-selfdecomposable or operator semi-selfdecomposable. In this paper, sequences of decreasing subclasses of the above
mentioned three classes,
, are introduced and several properties and characterizations are studied. The results obtained here are p-adic vector space versions of those given for probability measures on Euclidean spaces. |
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Keywords: | 2000 Mathematics Subject Classification: 60B15 60E07 60F05 |
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