Papers on journals or proceedings with a referee. Baldi P. B 10 , Recurrent Random Walks on certain classes of groups.

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Papers on journals or proceedings with a referee. Baldi P. B 10 , Recurrent Random Walks on certain classes of groups. Wahrscheinlichkeitstheorie verw. Gebiete 37 , Paris , B 12 , Sur la classification des groupes recurrents. B 14 , Notes Math. B 17 , Small Random Perturbations of Peano Phenomena.

Stochastics 6, Zeitschrift , Theory Relat. Fields 71 , Limit Set of inhomogeneous Ornstein- Uhlenbeck Processes.

Destabilization and Annealing. Processes Appl. Large Deviations and Stochastic Homogenization. In Stochastic Analysis rel. Topics II, Lect. Large Deviations and Strassen Law in Holder norm. Some exact equivalents for the Brownian motion in Holder norm. Fields 93, Entre la normalisation de Strassen et celle de Chung. Modulus of continuity for stochastic flows. Importance Sampling for Gibbs Random Fields. Andriani C. Sharp estimates of deviations of the sample mean. Abundo M. A diffusion approximation which models hierarchic interactions in cooperative biological systems.

Open Syst. Large and moderate deviations for random walks on nilpotent groups. Pricing single and double barrier options via Sharp Large Deviations techniques.

Finance 9, A representation formula for the large deviation rate function for the empirical law of a continuous time Markov chain. Letters 41 , Proceedings 3rd Int. Importance sampling for a continuous time Markov chain and applications to fluid models. Methodology Comp. Stable laws arising from hitting distributions of processes on homogeneous trees and the hyperbolic half-plane.

Pacific J. Asymptotics of hitting probabilities for general one-dimensional pinned diffusions. Bernoulli 12 , Letters 77, — On the characterization of isotropic Gaussian fields on homogeneous spaces of compact groups.

Electronic Comm. Marinucci D. Multivariate Analysis 99 , Asymptotics for Spherical Needlets. Subsampling Needlet Coefficients on the Sphere , Bernoulli 15 2 , Adaptive density estimation for directional data using needlets , Ann. Russo T. Biology , Progress in modelling herring populations: an individual-based model of growth.

Finance 16 , [15 pages] DOI: On Levy's Brownian motion indexed by the elements of compact groups, Colloq. DOI: Fourier coefficients of invariant random fields on homogeneous spaces of compact groups, Ann.

Large deviations of conditioned diffusions and applications, Stoch. Other publications. Class notes. Large Deviations. Notes appuntacci Random walk models and the simulation of rare events. Notes for the summer school SMI, Cortona Available in PDF. Equazioni Differenziali Stocastiche e Applicazioni. Quaderno U. Bologna, McGraw-Hill Italia, Milano, Appunti di Metodi Matematici e Statistici. Clueb Bologna, McGraw -Hill Italia , Milano, Hermann, Paris Mazliak L.

The McGraw-Hill Companies Stochastic Calculus, an introduction through theory and exercises. Springer Other publications Baldi P. Sur la Classification des Groupes Recurrents. Clermont Math. An Introduction to the Theory of Large Deviations. Milano 56, On the continuity of the Ito functional in strong topologies.

Importance sampling for continuous time Markov chains and applications to fluid models. Curie Paris 6 , New insight into growth parameters estimation: searching for a better approach in data massaging. I 8 I, Varadhan ha vinto il premio Abel per la matematica?


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Equazioni differenziali stocastiche e applicazioni

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Stochastic calculus

This is a standard course on the subject. The main arguments are Brownian motion, martingales, Ito integration and introduction to stochastic differential equations. This is the only course in advanced probability of the degree in mathematics, so from that point of view it must be and truly is self-contained. Nevertheless, since some topics are quite advanced, a thorough understanding of probability theory is an expected prerequisite. Gain a good theoretical understanding of stochastic processes and the ability to study simple stochastic differential equations in a qualitative and quantitative way, both in the field of pure research and in industrial applications for example in finance and in the modeling of noisy systems.


Stochastic equation of population dynamics with diffusion on a domain

Students are expected to acquire: basic knowledge of stochastic procesess and stochastic calculus, in particular Gaussian and Markov processes, Brownian motion and Poisson process, Martingales, stochastic integrals, Ito formula and elements of stochastic differential equations. The student should master both the basic arguments of probability such as basic probability, random variables, etc and some more andvanced topics such as measure theory with a view on probability , limit theorems. Definitions about stochastic processes, Kolmogorov extension theorem, Gaussian and Markov processes. Brownian motion and Poisson process: construction and path properties.

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