Corrigenda to "Operator semi-stable probability measures on $R^N$''

Łuczak, Andrzej

doi:10.4064/cm-52-1-167-169

Cited by 13 publications

(16 citation statements)

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“…The operator B is called a stability exponent of X. We refer to [3,13,20,22] and to the monograph [25] for more comprehensive information on operator semistable laws. As a consequence of (1), an operator semistable Lévy process X is also operator semiselfsimilar, i.e., for the constant c > 1 in (1),…”

Section: Introduction and Statement Of The Resultsmentioning

confidence: 99%

Multiple Points of Operator Semistable Lévy Processes

Luks

Xiao

2018

J Theor Probab

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We determine the Hausdorff dimension of the set of k-multiple points for a symmetric operator semistable Lévy process X = {X(t), t ∈ R + } in terms of the eigenvalues of its stability exponent. We also give a necessary and sufficient condition for the existence of k-multiple points. Our results extend to all k ≥ 2 the recent work [23], where the set of double points (k = 2) was studied in the symmetric operator stable case.2010 Mathematics Subject Classification. 60J25, 60J30, 60G51, 60G17.

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Section: Introduction and Statement Of The Resultsmentioning

confidence: 99%

Multiple Points of Operator Semistable Lévy Processes

Luks

Xiao

2018

J Theor Probab

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“…From the proof of Lemma 1.2 and Lemma 1.3 in [1], we can get the following lemmas. Our main result is the following theorem.…”

Section: Resultsmentioning

confidence: 99%

“…By the proof of Remark 1.1 in [1], we can get the following proposition. By the proof of Remark 1.1 in [1], we can get the following proposition.…”

Section: Definitionmentioning

confidence: 85%

Operator Semi-Stable Distributions

Wang

2005

Stochastic Analysis and Applications

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Jajte introduced the operator semi-stable distributions on R n in [2] and proved an important fact: A full distribution is operator semi-stable, if and only if, there exist a number c 0 < c < 1 , a vector h ∈ R n , and a nonsingular linear operator B in R n such that the formula c = B * h holds. In this paper, we make use of the eigenvalue of the matrix B to give a necessary and sufficient condition for x ≤1 x r M dx < , where M is the Lévy measure of . Also, we use the symmetric group of to characterize the operators B in (1).

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“…The Lévy process X is called operator semistable if the (infinitely divisible) distribution µ of X(1) is full, i.e. not supported on any lower dimensional hyperplane, and fulfills further early investigations can be found in [20,21,7]. In case u = 0 the distribution µ, respectively the Lévy process X generated by µ, is called strictly operator semistable.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic Behavior of Semistable Lévy Exponents and Applications to Fractal Path Properties

2016

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This paper proves sharp bounds on the tails of the Lévy exponent of an operator semistable law on R d . These bounds are then applied to explicitly compute the Hausdorff and packing dimensions of the range, graph, and other random sets describing the sample paths of the corresponding operator semi-selfsimilar Lévy processes. The proofs are elementary, using only the properties of the Lévy exponent, and certain index formulae.E n , and ε u denotes the Dirac measure at the point u ∈ R d . Operator semistable distributions were introduced by Jajte [12];

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Corrigenda to "Operator semi-stable probability measures on $R^N$''

Cited by 13 publications

References 0 publications

Multiple Points of Operator Semistable Lévy Processes

Multiple Points of Operator Semistable Lévy Processes

Operator Semi-Stable Distributions

Asymptotic Behavior of Semistable Lévy Exponents and Applications to Fractal Path Properties

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