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- B. Boufoussi, Marco Dozzi
- 2005

Let (B(t), t ∈ R) be a multifractional Brownian motion with Hurst functional H(.) ∈ C(R, (0, 1)). Under mild regularity conditions on H, the existence, the joint continuity and the Hölder regularity of the local time of B are proved. The local Hausdorff dimension of the level sets of B is determined.

Backward stochastic differential equations (BSDEs) were introduced by Pardoux and Peng [6], and it was shown in various papers that stochastic differential equations (SDEs) of this type give a probabilistic representation for the solution (at least in the viscosity sense) of a large class of system of semi-linear parabolic partial differential equations… (More)

Various paths properties of a stochastic process are obtained under mild conditions which allow for the integrability of the characteristic function of its increments and for the dependence among them. The main assumption is closely related to the notion of local asymptotic self-similarity. New results are obtained for the class of multifractional random… (More)

- B. Boufoussi, S. Hajji
- Computers & Mathematics with Applications
- 2011

In this paper we consider a class of time-dependent neutral stochastic functional differential equations with finite delay driven by a fractional Brownian motion with Hurst parameter H ∈ ( 1 2 , 1), in a separable real Hilbert space. We prove an existence and uniqueness result of mild solution by means of the Banach fixed point principle. A practical… (More)

The stochastic calculus for Gaussian processes is applied to obtain a Tanaka formula for a Volterra-type multifractional Gaussian process. The existence and the regularity properties of the local time of this process is obtained by means of Berman’s Fourier analytic approach.

- BRAHIM BOUFOUSSI, RABY GUERBAZ
- 2007

Multifractional Brownian motion (mBm), B = (B(t), t ∈ R), is a Gaussian process which extends fractional Brownian motion (fBm) by allowing the Hurst function to vary with time. This provides a tool to model systems whose regularity evolves over time, such as internet traffic or images. Recently, Boufoussi et al. [6] have investigated, under mild regularity… (More)

By using successive approximation, we prove existence and uniqueness result for a class of neutral functional stochastic differential equations in Hilbert spaces with non-Lipschitzian coefficients Approximations successives pour les équations fonctionelles stochastiques de type neutre dans un espace de Hilbert. Résumé En utilisant la méthode des… (More)

Let {B t , t ∈ [0, T ]} be a fractional Brownian motion with Hurst parameter H > 1 2 . We prove the existence of a weak solution for a stochastic differential equation of the form Xt = x+B t + ∫ t 0 (b1(s,Xs) + b2(s,Xs)) ds, where b1(s, x) is a Hölder continuous function of order strictly larger than 1− 1 2H in x and than H− 1 2 in time and b2 is a real… (More)

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