The generalized sub-fractional Brownian motion

Sghir, Aissa

doi:10.31390/cosa.7.3.02

Cited by 6 publications

(3 citation statements)

References 5 publications

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“…(1) The process X H has infinitely differentiable trajectories and it is well-known that in this case the local time does not exist because the occupation measure is singular. (2) We believe that the same arguments used in this paper can be used for the bifractional Brownian motion and the Gaussian process introduced in Sghir [12].…”

Section: Proof By Virtue Of the Elementary Inequality (A + B)mentioning

confidence: 79%

Local time of a multifractional Gaussian process

Sghir¹

2013

COSA

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Abstract. In this paper, a new multifractional Gaussian process is defined by a integral representation. We prove an approximation in law of this process and we prove that the covariance function of this process permits us to obtain a generalization of the sub-fractional Brownian motion [5] by a decomposition in law into the sum of our process and the standard multifractional Brownian motion [1]. We prove also the existence and the joint continuity of the local time of our process.

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Section: Proof By Virtue Of the Elementary Inequality (A + B)mentioning

confidence: 79%

Local time of a multifractional Gaussian process

Sghir¹

2013

COSA

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“…One extension of the sfBm was introduced in [9] and called the generalized subfractional Brownian motion (GsfBm). It is a centered Gaussian process starting from zero with covariance function…”

Section: Introductionmentioning

confidence: 99%

Generalized fractional Brownian motion

Zili¹

2017

Modern Stoch. Theory Appl.

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We introduce a new Gaussian process, a generalization of both fractional and subfractional Brownian motions, which could serve as a good model for a larger class of natural phenomena. We study its main stochastic properties and some increments characteristics. As an application, we deduce the properties of nonsemimartingality, Hölder continuity, nondifferentiablity, and existence of a local time.

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“…✷ 2.6 Example. Generalized sub-fractional Brownian motions were introduced by Sghir [17]. In one of the representation theorems of Sghir [17, Theorem 2.2], a self-similar process comes into play that can be generalized to present another example for a dilatively stable generalized fractional Lévy process as follows.…”

Section: Then (S (H) Tmentioning

confidence: 99%

Dilatively stable stochastic processes and aggregate similarity

2014

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Dilatively stable processes generalize the class of infinitely divisible self-similar processes. We reformulate and extend the definition of dilative stability introduced by Iglói (2008) using characteristic functions. We also generalize the concept of aggregate similarity introduced by Kaj (2005). It turns out that these two notions are essentially the same for infinitely divisible processes. Examples of dilatively stable generalized fractional Lévy processes are given and we point out that certain limit processes in aggregation models are dilatively stable.

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The generalized sub-fractional Brownian motion

Cited by 6 publications

References 5 publications

Local time of a multifractional Gaussian process

Local time of a multifractional Gaussian process

Generalized fractional Brownian motion

Dilatively stable stochastic processes and aggregate similarity

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