MOUNIR ZILI
University of Monastir, Mathematics, Department Member
- Professor Mounir Zili, Mathematician A Bridge-Builder Across Academia, Sustainability and Employability Un bâtisseu... moreProfessor Mounir Zili, Mathematician
A Bridge-Builder Across Academia, Sustainability and Employability
Un bâtisseur de ponts entre l'université, le développement durable et l'employabilité
Professor Mounir Zili, a distinguished Tunisian researcher, has carved a remarkable career at the confluence of mathematics, environmental sustainability, and employability. His expertise lies in stochastic analysis, a branch of mathematics that deals with random phenomena.
Zili's academic journey commenced with a Ph.D. in 1996 from the prestigious University Paris VI "Pierre et Marie Curie" in France. His doctoral dissertation delved into a complex topic: fundamental solutions of parabolic partial differential equations with nonsmooth coefficients. He further explored the connection between these equations and stochastic differential equations.
Currently a Full Professor in the Department of University Studies at the Military Academy Foundok Jedid, Tunisia, M. Zili actively contributes to research through the Laboratory research LR18ES17 at the Faculty of Sciences of the University of Monastir. He also leads the scientific association Monastir Living-Lab.
Professor Zili's research prowess is evident in his four well-regarded books on probability and stochastic analysis, published by renowned publishers like Springer-Verlag, ISTE Wiley, and ISTE Press Elsevier. His contributions extend beyond publications, as he serves as a reviewer for several esteemed scientific journals, ensuring the quality and rigor of published research.
A passionate educator, Zili nurtures the next generation of researchers. He has guided five Ph.D. and five Master's theses, all focused on stochastic processes and their applications in finance. His commitment to knowledge dissemination extends beyond the classroom. He has organized two international conferences on stochastic analysis, providing a platform for researchers from 15 countries across five continents to share their expertise.
Mounir Zili's leadership spans both academic and administrative domains. He previously served as the head of the Department of Mathematics at the Preparatory School for Military Academies and as head of a research unit within the same institution. At the Faculty of Sciences of the University of Monastir, his dedication to fostering academic excellence is further evident by his past tenure as the Head of the Research Master's Commission of Maths, member of the scientific council, and his participation as president and member of numerous Ph.D. and Master's juries.
Since 2017, Professor Zili has presided over Monastir Living-Lab, a scientific association dedicated to promoting local development through innovation and research. Under his leadership, the association's activities have focused on addressing environmental challenges and implementing sustainable waste management practices.
Through Monastir Living-Lab, Zili has organized two national conferences on innovative waste management strategies for local development. He has also supervised three professional master's theses on methanization, a process that converts organic waste into biogas.
Mounir Zili's commitment to employability is further demonstrated by his participation in the UK Study Tour-MENA: Regional Employability: Midlands and Wales in 2013. This experience equipped him with valuable insights on connecting academia with industry, economy an society needs.
Professor Zili exemplifies the power of bridging academic disciplines, sustainability, and employability. His unwavering pursuit of knowledge in mathematics is complemented by his commitment to environmental solutions and his dedication to preparing students for success in the global workforce. As he continues his work, Professor Zili remains a true inspiration for researchers, sustainability advocates, and educators alike.edit
Research Interests: Mathematics, Applied Mathematics, Stochastic Process, Monte Carlo Simulation, Monte Carlo, and 14 moreFractals, Estimation Theory, Differential Equations, Monte Carlo Methods, Parameter estimation, Stochastic processes, Brownian Motion, Fractional Brownian Motion, Maximum Likelihood Estimation, Stochastic differential equation, Estimation Method, Monte Carlo Method, Hurst Exponent, and Hurst Parameter
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Preface.- 1.H. Schurz: Basic Concepts of Numerical Analysis of Stochastic Differential Equations Explained by Balanced Implicit Theta Methods .- 2.C.A. Tudor: Kernel Density Estimation, Local Time and Chaos Expansion.- 3.W. Jedidi, J.... more
Preface.- 1.H. Schurz: Basic Concepts of Numerical Analysis of Stochastic Differential Equations Explained by Balanced Implicit Theta Methods .- 2.C.A. Tudor: Kernel Density Estimation, Local Time and Chaos Expansion.- 3.W. Jedidi, J. Almhana, V. Choulakian, R. McGorman: General Shot Noise Processes and Functional Convergence to Stable Processes.- 4.C. El-Nouty: The Lower Classes of the Sub-Fractional Brownian Motion.- 5.M. Erraoui and Y. Ouknine: On the Bounded Variation of the Flow of Stochastic Differential Equation.- 6.A. Ayache, Q. Peng: Stochastic Volatility and Multifractional Brownian Motion.- 7.A. Gulisashvili, J. Vives: Two-sided Estimates for Distribution Densities in Models with Jumps.- 8.M. Lefebvre: Maximizing a Function of the Survival Time of a Wiener Process in an Interval.
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We study a second-order parabolic equation with divergence form elliptic operator, having piecewise constant diffusion coefficients with two points of discontinuity. Such partial differential equations appear in the modelization of... more
We study a second-order parabolic equation with divergence form elliptic operator, having piecewise constant diffusion coefficients with two points of discontinuity. Such partial differential equations appear in the modelization of diffusion phenomena in medium consisting of three kind of materials. Using probabilistic methods, we present an explicit expression of the fundamental solution under certain conditions. We also derive small-time asymptotic expansion of the PDE's solutions in the general case. The obtained results are directly usable in applications.
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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 space-time white noise. We introduce a notion of weak... more
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 space-time white noise. We introduce a notion of weak solution of this equation and prove its equivalence to the already known notion of mild solution.
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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 motions, that we have chosen to call the mixed sub-fractional... more
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 motions, that we have chosen to call the mixed sub-fractional Brownian motion. In this paper, we study some basic properties of this process, its non-Markovian and non-stationarity characteristics, the conditions under which it is a semimartingale, and the main features of its sample paths. We also show that this process could serve to get a good model of certain phenomena, taking not only the sign (like in the case of the sub-fractional Brownian motion), but also the strength of dependence between the increments of this phenomena into account.
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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 noise. Such SPDEs could be used in mathematical modelling of... more
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 noise. Such SPDEs could be used in mathematical modelling of diffusion phenomena in medium consisting of different kinds of materials and undergoing stochastic perturbations. We characterize the solution and, using the Stein--Malliavin calculus, we prove that the sequence of its recentered and renormalized spatial quadratic variations satisfies an almost sure central limit theorem. Particular focus is given to the interesting case where the coefficients of the operator are piecewise constant.
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Dans ce travail, en utilisant des methodes stochastiques, on presente un developpement asymptotique en temps petits de la solution d'une equation aux derivees partielles generalisee au sens des distributions-mesures.
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Let ${S_t^H, t \geq 0} $ be a linear combination of a Brownian motion and of an independent sub-fractional Brownian motion with Hurst index $0 < H < 1$. Its main properties are studied and it is shown that $S^H $ can be considered... more
Let ${S_t^H, t \geq 0} $ be a linear combination of a Brownian motion and of an independent sub-fractional Brownian motion with Hurst index $0 < H < 1$. Its main properties are studied and it is shown that $S^H $ can be considered as an intermediate process between a sub-fractional Brownian motion and a mixed fractional Brownian motion. Finally, we determine the values of $H$ for which $S^H$ is not a semi-martingale.
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Our aim is in conceiving innovative processes in the whole recycling value chain, including the waste treatment fields in the objective to economize water, energy and to create clean and safe environment in the main establishments of the... more
Our aim is in conceiving innovative processes in the whole recycling value chain, including the waste treatment fields in the objective to economize water, energy and to create clean and safe environment in the main establishments of the University of Monastir and in the City of Monastir. The main mission is to establish circular economy concept by creating a sustainable development, based on research, innovation, cooperation and participation. The main objectives of the Monastir living Lab (MoLL)is to widespread the good practices from the smart campus to the smart City! The strengths of Monastir Living Lab are the existance of an important synergy between research, industrial and societal activities, especially in textile and fashion domains, chemistry, water treatment, energetics, electro-mechanics, biotechnology and health science. The University of Monastir campus is essentially based on an important collaborations and projects with industry in textile, packaging, electric-elec...
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We present an explicit series expansion of the sub-mixed fractional Brownian motion and study its rate of convergence. We show that the obtained expansion is rate-optimal in the sense that the expected uniform norm of the truncated series... more
We present an explicit series expansion of the sub-mixed fractional Brownian motion and study its rate of convergence. We show that the obtained expansion is rate-optimal in the sense that the expected uniform norm of the truncated series vanishes at optimal rate as the truncation point tends to infinity. As an application of this result, we present a computer generation of sample paths for sub-mixed fractional Brownian motion.
We study the asymptotic behavior of the spatial quadratic variation for the solution to the stochastic wave equation driven by additive space-time white noise. We prove that the sequence of its renormalized quadratic variations satisfies... more
We study the asymptotic behavior of the spatial quadratic variation for the solution to the stochastic wave equation driven by additive space-time white noise. We prove that the sequence of its renormalized quadratic variations satisfies a central limit theorem (CLT for short). We obtain the rate of convergence for this CLT via the Stein–Malliavin calculus and we also discuss some consequences.
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We introduce a new stochastic heat equation with a colored-white fractional noise, which behaves as a Wiener process in the spatial variable and as mixed sub-fractional Brownian motion in time. A necessary and sufficient condition for the... more
We introduce a new stochastic heat equation with a colored-white fractional noise, which behaves as a Wiener process in the spatial variable and as mixed sub-fractional Brownian motion in time. A necessary and sufficient condition for the existence of its solution is reported. We also analyze regularity properties of this equation, with respect to the temporal and spatial variables, respectively. Some fractal dimensions of the graphs and ranges of the associated sample paths are determined.
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Daria Filatova*, Marek Grzywaczewski, Elizaveta Shybanova and Mounir Zili** * Analytical Centre, Russian Academy of Sciences, Moscow, Russia, e-mail: daria_filatova@interia.pl Institute of Mathematics, Technical University, Radom,... more
Daria Filatova*, Marek Grzywaczewski, Elizaveta Shybanova and Mounir Zili** * Analytical Centre, Russian Academy of Sciences, Moscow, Russia, e-mail: daria_filatova@interia.pl Institute of Mathematics, Technical University, Radom, Poland, e-mail: mgrzyw@interia.pl ...
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The mixed fractional Brownian motion is used in mathematical finance, in the modelling of some arbitrage-free and complete markets. In this paper, we present some stochastic properties and characteristics of this process, and we study... more
The mixed fractional Brownian motion is used in mathematical finance, in the modelling of some arbitrage-free and complete markets. In this paper, we present some stochastic properties and characteristics of this process, and we study theα-differentiability of its sample paths.
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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 infinite-dimensional fractional Brownian motion. We... more
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 infinite-dimensional fractional Brownian motion. We characterize the fundamental solution of its deterministic part, and prove the existence and the uniqueness of its solution.
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In 1962 Lamperti introduced a transformation that associates to every non-trivial self-similar process a strictly stationary process. This transform has been widely studied for Gaussian processes and in particular for fractional Brownian... more
In 1962 Lamperti introduced a transformation that associates to every non-trivial self-similar process a strictly stationary process. This transform has been widely studied for Gaussian processes and in particular for fractional Brownian motion. Our aim is to analyze various properties of the Lamperti transform of the fractional Brownian sheet. We give the stochastic differential equation satisfied by this transform and we represent it as a series of independent Ornstein-Uhlenbeck sheets.
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We present an explicit series expansion of the sub-mixed fractional Brownian motion and study its rate of convergence. We show that the obtained expansion is rate-optimal in the sense that the expected uniform norm of the truncated series... more
We present an explicit series expansion of the sub-mixed fractional Brownian motion and study its rate of convergence. We show that the obtained expansion is rate-optimal in the sense that the expected uniform norm of the truncated series vanishes at optimal rate as the truncation point tends to infinity. As an application of this result, we present a computer generation of sample paths for sub-mixed fractional Brownian motion.
Portfolio Optimization Problem of Mertons' Market Driven by a Fractional Brownian Motion.
The author considers a stochastic differential equation driven by a Brownian motion, with an elliptic diffusion coefficient. He does not suppose that the coefficients are continuous, but that there exists a unique solution (uniqueness is... more
The author considers a stochastic differential equation driven by a Brownian motion, with an elliptic diffusion coefficient. He does not suppose that the coefficients are continuous, but that there exists a unique solution (uniqueness is understood in pathwise sense). He proves that the approximation obtained by introducing a delay in the coefficients (Carathéodory approximation) converges to the solution. Then he applies this result to an equation involving a local time.
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We prove the pathwise uniqueness of solutions of a stochastic differential equation with a singular drift which depends on time. Our method is of probabilistic nature, and it is based on an Al-Hussaini and Elliott result.