Continuity in law of some additive functionals of bifractional Brownian motion

Ouahra, M. Ait; Ouahhabi, Hanae; Sghir, Aissa

doi:10.1080/17442508.2019.1568436

Cited by 5 publications

(5 citation statements)

References 25 publications

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“…We know by [1,Lemma 3.3] (see also [24]) that the process (B α,β (t)) t 0 is locally non-deterministic, i.e. for all…”

Section: Besov Regularity Of the Bifractional Brownian Motionmentioning

confidence: 99%

On the Besov regularity of the bifractional Brownian motion

Boufoussi¹,

Nachit²

2020

PMS

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Our aim is to improve Hölder continuity results for the bifractional Brownian motion (bBm) (B α,β (t)) t∈[0,1] with 0 < α < 1 and 0 < β 1. We prove that almost all paths of the bBm belong to (resp. do not belong to) the Besov spaces Bes(αβ, p) (resp. bes(αβ, p)) for any 1 αβ < p < ∞, where bes(αβ, p) is a separable subspace of Bes(αβ, p). We also show similar regularity results in the Besov-Orlicz space Bes(αβ, M2) with M2(x) = e x 2 − 1. We conclude by proving the Itô-Nisio theorem for the bBm with αβ > 1/2 in the Hölder spaces C γ with γ < αβ.

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“…We know by [1,Lemma 3.3] (see also [24]) that the process (B α,β (t)) t 0 is locally non-deterministic, i.e. for all…”

Section: Besov Regularity Of the Bifractional Brownian Motionmentioning

confidence: 99%

On the Besov regularity of the bifractional Brownian motion

Boufoussi¹,

Nachit²

2020

PMS

View full text Add to dashboard Cite

show abstract

“…We know by [1,Lemma 3.3] (In this last article to prove the local-nondeterminism of the bBm the authors use the same techniques as those of [18]) that the process (B α,β (t)) t≥0 is locally non-deterministic i.e. for all 0 = t 0 < t 1 < ... < t m < 1 with…”

Section: Besov Regularity Of the Bifractional Brownian Motionmentioning

confidence: 99%

“…The third paragraph is devoted to study the Besov regularity for the sample paths of the bifractional Brownian motion. In the fourth paragraph we investigate the Itô-Nisio theorem for bBm with αβ > 1 2 . The proofs of our results use technical and very fine calculations based on dyadic coordinate expansions of the bifractional Brownian motion and descriptions of the Besov norms in terms of the corresponding expansion coefficients of a function.…”

Section: Introductionmentioning

confidence: 99%

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On the Besov regularity of the bifractional Brownian motion

Boufoussi¹,

Nachit²

2020

Preprint

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Our aim in this paper is to improve Hölder continuity results for the bifractional Brownian motion (bBm) (B α,β (t)) t∈[0,1] with 0 < α < 1 and 0 < β ≤ 1. We prove that almost all paths of the bBm belong (resp. do not belong) to the Besov spaces Bes(αβ, p) (resp. bes(αβ, p)) for any 1 αβ < p < ∞, where bes(αβ, p) is a separable subspace of Bes(αβ, p). We also show the Itô-Nisio theorem for the bBm with αβ > 1 2 in the Hölder spaces C γ , with γ < αβ.

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“…Xu [51] proposed a pricing model for European options and compound options in the BFBM environment and derived the pricing formulae by the method of variable substitution and risk-neutral principle. More discussions of the BFBM could be seen in references [52][53][54][55][56] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Pricing Vulnerable Options in the Bifractional Brownian Environment with Jumps

Cheng

2021

Journal of Mathematics

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In this paper, we study the valuation of European vulnerable options where the underlying asset price and the firm value of the counterparty both follow the bifractional Brownian motion with jumps, respectively. We assume that default event occurs when the firm value of the counterparty is less than the default boundary. By using the actuarial approach, analytic formulae for pricing the European vulnerable options are derived. The proposed pricing model contains many existing models such as Black–Scholes model (1973), Merton jump-diffusion model (1976), Klein model (1996), and Tian et al. model (2014).

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Continuity in law of some additive functionals of bifractional Brownian motion

Cited by 5 publications

References 25 publications

On the Besov regularity of the bifractional Brownian motion

On the Besov regularity of the bifractional Brownian motion

On the Besov regularity of the bifractional Brownian motion

Pricing Vulnerable Options in the Bifractional Brownian Environment with Jumps

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