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- B. Boufoussi, Marco Dozzi
- 2005

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

In this paper a new class of generalized backward doubly stochastic differential equations is investigated. This class involves an integral with respect to an adapted continuous increasing process. A probabilistic representation for viscosity solutions of semi-linear stochastic partial differential equations with a Neumann boundary condition is given.

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 investigate the existence and stability of quadratic-mean almost periodic mild solutions to stochastic delay functional differential equations driven by fractional Brownian motion with Hurst parameter H > 1 2 , under some suitable assumptions, by means of semigroup of operators and fixed point method.

- BRAHIM BOUFOUSSI, RABY GUERBAZ
- 2007

We establish estimates for the local and uniform moduli of continuity of the local time of multifractional Brownian motion, B H = (B H(t) (t), t ∈ R +). An analogue of Chung's law of the iterated logarithm is studied for B H and used to obtain the pointwise Hölder exponent of the local time. A kind of local asymptotic self-similarity is proved to be… (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.

Let {B H 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 X t = x + B H t + t 0 (b 1 (s, X s) + b 2 (s, X s)) ds, where b 1 (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… (More)

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