Levi-Civita,Tullio

International audienceTullio Levi-Civita (29 March 1873 to 29 December 1941) has been an Italian mathematician and mathematical physicist, known above all for his work on the absolute differential calculus. Levi-Civita came from a rigorous and creative school of mathematical physicists and was a pupil of Gregorio Ricci-Curbastro. LeviCivita’s work included outstanding results in pure and applied mathematics and in celestial and analytic mechanics but also celebrated textbooks. These last, even those written in Italian, have influenced mathematical physicists all over the world.Levi-Civita has perfected some conceptual tools of great importance in modern science, particularly in general relativity, number theory, and continuum mechanics

Controlled trees

The control of branching processes has been studied in several papers (E 1981; Ustunel, 1981). However, in these works, the authors used methods for the markovian case and they were obliged to consider the global evol the particle system: it was not possible to control every particle. In this paper, we define the notion of controlled tree, where the contr further mark on the tree. We then introduce a control problem for this tree

A multidimensional bipolar theorem in

In this paper, we prove a multidimensional extension of the so-called Bipolar Theorem proved in Brannath and Schachermayer (Séminaire de Probabilités, vol. XXX, 1999, p. 349), which says that the bipolar of a convex set of positive random variables is equal to its closed, solid convex hull. This result may be seen as an extension of the classical statement that the bipolar of a subset in a locally convex vector space equals its convex hull. The proof in Brannath and Schachermayer (ibidem) is strongly dependent on the order properties of . Here, we define a (partial) order structure with respect to a d-dimensional convex cone K of the positive orthant [0,[infinity])d. We may then use compactness properties to work with the first component and obtain the result for convex subsets of K-valued random variables from the theorem of Brannath and Schachermayer (ibidem). As a byproduct, we obtain an equivalence property for a class of minimization problems in the spirit of Kramkov and Schachermayer (Ann. Appl. Probab 9(3) (1999) 904, Proposition 3.2). Finally, we discuss some applications in the context of duality theory of the utility maximization problem in financial markets with proportional transaction costs.Polarity Convex analysis Partial order Convergence in probability Dual formulation in mathematical finance

Optimal Design in Nonparametric Life Testing

stochastic control, point process, nonparametric estimation,