Mesures gaussiennes et mesures produits
Metastable behaviour of small noise Lévy-Driven diffusions
We consider a dynamical system in driven by a vector field -U', where U is a multi-well potential satisfying some regularity conditions. We perturb this dynamical system by a Lévy noise of small intensity and such that the heaviest tail of its Lévy measure is regularly varying. We show that the perturbed dynamical system exhibits metastable behaviour i.e. on a proper time scale it reminds of a Markov jump process taking values in the local minima of the potential U. Due to the heavy-tail nature...
Metric entropy and the central limit theorem in
Central limit theorems with hypotheses in terms of -entropy are proved first in where is a compact metric space and then in an arbitrary separable Banach space.
Metric properties of alternating Lüroth series
Metric results on a new notion of discrepancy
Metric Theorems Related to the Kronecker - Weyl Theorem mod m.
Mild law of large numbers and its consequences
Milstein’s type schemes for fractional SDEs
Weighted power variations of fractional brownian motion B are used to compute the exact rate of convergence of some approximating schemes associated to one-dimensional stochastic differential equations (SDEs) driven by B. The limit of the error between the exact solution and the considered scheme is computed explicitly.
Minimization of the Kullback information for some Markov processes
Minimization of the Kullback information of diffusion processes
Minimum variance importance sampling via Population Monte Carlo
Variance reduction has always been a central issue in Monte Carlo experiments. Population Monte Carlo can be used to this effect, in that a mixture of importance functions, called a D-kernel, can be iteratively optimized to achieve the minimum asymptotic variance for a function of interest among all possible mixtures. The implementation of this iterative scheme is illustrated for the computation of the price of a European option in the Cox-Ingersoll-Ross model. A Central Limit theorem as well...
Modèles statistiques et systèmes standards de processus de vraisemblance
Models for option pricing based on empirical characteristic function of returns
The standard Merton-Black-Scholes formula for European Option pricing serves only as approximation to real values of options. More advanced extensions include applications of Lévy processes and are based on characteristic functions, which are more convenient to use than the corresponding probability distributions. We found one of the Lewis (2001) general theoretical formulae for option pricing based on characteristic functions particularly suitable for a statistical approach to option pricing. By...
Moderate deviation principles for sums of i.i.d. random compact sets
We prove a moderate deviation principle for Minkowski sums of i.i.d. random compact sets in a Banach space.
Moderate deviations and laws of the iterated logarithm for the renormalized self-intersection local times of planar random walks.
Moderate deviations and laws of the iterated logarithm for the volume of the intersections of Wiener sausages.
Moderate deviations for a Curie–Weiss model with dynamical external field
In the present paper we prove moderate deviations for a Curie–Weiss model with external magnetic field generated by a dynamical system, as introduced by Dombry and Guillotin-Plantard in [C. Dombry and N. Guillotin-Plantard, Markov Process. Related Fields 15 (2009) 1–30]. The results extend those already obtained for the Curie–Weiss model without external field by Eichelsbacher and Löwe in [P. Eichelsbacher and M. Löwe, Markov Process. Related Fields 10 (2004) 345–366]. The Curie–Weiss model with...
Moderate deviations for bounded subsequences.
Moderate deviations for diffusions in a random gaussian shear flow drift
Moderate deviations for functional U-processes