20 citations · 32 across the 6 of their papers we have counts for
8 papers
On mild and weak solutions for stochastic heat equations with piecewise-constant conductivity
Yuliya Mishura, Kostiantyn Ralchenko, Mounir Zili
We investigate a stochastic partial differential equation with second order elliptic operator in divergence form, having a piecewise constant diffusion coefficient, and driven by a…
Spatial quadratic variations for the solution to a stochastic partial differential equation with elliptic divergence form operator
Mounir Zili, Eya Zougar
We introduce a stochastic partial differential equation (SPDE) with elliptic operator in divergence form, with measurable and bounded coefficients and driven by space-time white no…
Fractional stochastic heat equation with piecewise constant coefficients
Yuliya Mishura, Kostiantyn Ralchenko, Mounir Zili +1
We introduce a fractional stochastic heat equation with second order elliptic operator in divergence form, having a piecewise constant diffusion coefficient, and driven by an infin…
Generalized fractional Brownian motion
Mounir Zili
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 phenome…
Drift parameter estimation in stochastic differential equation with multiplicative stochastic volatility
Meriem Bel Hadj Khlifa, Yuliya Mishura, Kostiantyn Ralchenko +1
We consider a stochastic differential equation of the form \[dX_t=θa(t,X_t)\,dt+σ_1(t,X_t)σ_2(t,Y_t)\,dW_t\] with multiplicative stochastic volatility, where is some adapted st…
One-dimensional heat equation with discontinuous conductance
Zhen-Qing Chen, Mounir Zili
We study a second-order parabolic equation with divergence form elliptic operator, having piecewise constant diffusion coefficients with two points of discontinuity. Such partial d…
Mixed Sub-Fractional Brownian Motion
Mounir Zili
A new extension of the sub-fractional Brownian motion, and thus of the Brownian motion, is introduced. It is a linear combination of a finite number of sub-fractional Brownian moti…
On the sub-mixed fractional Brownian motion
Charles El-Nouty, Mounir Zili
Let be a linear combination of a Brownian motion and of an independent sub-fractional Brownian motion with Hurst index . Its main properties are stu…