Convergence in law for certain additive functionals of symmetric stable processes under strong topology

Ouahra, M. Ait

doi:10.1016/j.crma.2005.02.013

Cited by 2 publications

(4 citation statements)

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“…(ii) A similar regularity is given in [1], more precisely, we notice that this regularity is not identical to that of our paper. To prove our result we need the regularity acting on , and the exponent of the temporal variable is independent of .…”

Section: Remark 32supporting

confidence: 58%

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On fractional derivatives of the local time of a symmetric stable process as a doubly indexed process

Ouahra

Kissami

Ouahhabi

2014

Random Operators and Stochastic Equations

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In this paper we prove two main results. The rst one is to prove the regularity of fractional derivatives of local time of symmetric stable process with index 1 < ≤ 2. Our result is similar to that of Marcus and Rosen in 1992 for local time. The second result is to give a ( , )-variation of fractional derivatives of local time of symmetric stable process with index 1 < ≤ 2. Our approach is similar to that of Eisenbaum in 2000 for local time.

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Section: Remark 32supporting

confidence: 58%

“…Let ( , ≥ 0) be a symmetric stable process with index in (1,2]. It is well known that this process is a real valued process with stationary independent increments such that = − | | , ∈ ℝ.…”

Section: Introductionmentioning

confidence: 99%

On fractional derivatives of the local time of a symmetric stable process as a doubly indexed process

Ouahra

Kissami

Ouahhabi

2014

Random Operators and Stochastic Equations

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“…The following hold:(i) Using similar calculations as in Theorem 1 of Ait Ouahra[1], we may easily prove that theorem for D 0, with the condition x; y 2 OE M; M for any M 0.…”

mentioning

confidence: 83%

“…Since the local time .L x t ; x 2 R; t 0/ of the symmetric stable process X D .X t ; t 0/ with index 1 <ˇÄ 2 is a ı-Hölder continuous function Brought to you by | University of Manitoba Authenticated Download Date | 6/9/15 9:40 AM with 0 < ı <ˇ 1 2 , in the space variable, its fractional derivative is given by…”

Section: Preliminaries and Notationsmentioning

confidence: 99%

On fractional derivatives of the local time of a symmetric stable process as a doubly indexed process

Ouahra

Kissami

Ouahhabi

2012

Random Operators and Stochastic Equations

Self Cite

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In this paper, we prove two main results. The first one is to prove the regularity of fractional derivatives of local time of symmetric stable process with index 1 <ˇÄ 2; our result is similar to that of Marcus and Rosen (1992) for local time. The second result is to give a p; q-variation of fractional derivatives of local time of symmetric stable process with index 1 <ˇÄ 2. Our approach is similar to that of Eisenbaum (2000) for local time.

show abstract

Convergence in law for certain additive functionals of symmetric stable processes under strong topology

Cited by 2 publications

References 10 publications

On fractional derivatives of the local time of a symmetric stable process as a doubly indexed process

On fractional derivatives of the local time of a symmetric stable process as a doubly indexed process

On fractional derivatives of the local time of a symmetric stable process as a doubly indexed process

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