IV: 10, 108-131, LNM 124 (1970)
FUCHS, Aimé;
LETTA, Giorgio
L'inégalité de Kullback. Application à la théorie de l'estimation (
Information theory,
Mathematical statistics)
This paper brings together, and shows the mutual relation of a number of classical definitions, centering on Shannon's mutual information of two probability measures, $G(\lambda|\mu)=\int \log {d\lambda\over d\mu}\,d\mu$
Comment: To be asked from the authors
Keywords: Kullback inequality,
Cramer-Rao inequality,
Sufficient statisticsNature: Original
Retrieve article from Numdam
IV: 19, 240-282, LNM 124 (1970)
DELLACHERIE, Claude;
DOLÉANS-DADE, Catherine;
LETTA, Giorgio;
MEYER, Paul-André
Diffusions à coefficients continus, d'après Stroock et Varadhan (
Markov processes,
Diffusion theory)
This paper consists of four seminar talks on a celebrated paper of Stroock-Varadhan (
Comm. Pure Appl. Math.,
22, 1969), which constructs by a probability method a unique semigroup whose generator is an elliptic second order operator with continuous coefficients (the analytic approach either deals with operators in divergence form, or requires some Hölder condition). The contribution of G.~Letta nicely simplified the proof
Comment: The results were so definitive that apparently the subject attracted no further work. See Stroock-Varadhan,
Multidimensional Diffusion Processes, Springer 1979
Keywords: Elliptic differential operators,
Uniqueness in lawNature: Exposition Retrieve article from Numdam
XII: 60, 804-805, LNM 649 (1978)
LETTA, Giorgio
Un système de notations pour les processus de Markov (
Markov processes)
Instead of notations like $X_T$, $\Theta_T$, etc, the author suggests to use kernel notations---for instance, $X^T$ is the submarkovian kernel $f\mapsto f\circ X_T$ ($0$ on $\{T=\infty\}$). Then the main properties of Markov processes are expressed by simple kernel equalities
Nature: Original Retrieve article from Numdam
XIII: 17, 216-226, LNM 721 (1979)
LETTA, Giorgio
Quasimartingales et formes linéaires associées (
General theory of processes,
Martingale theory)
This paper gives a definition of a quasimartingale $X$ different from the usual one using the stochastic variation: the linear functional $E[\int_0^{\infty} H_s dX_s]$ should be relatively bounded on the vector lattice (Riesz space) of elementary previsible processes. Many classical theorems have simple proofs or elegant interpretations in this language
Keywords: Quasimartingales,
Riesz spacesNature: Original Retrieve article from Numdam
XX: 02, 28-29, LNM 1204 (1986)
FAGNOLA, Franco;
LETTA, Giorgio
Sur la représentation intégrale des martingales du processus de Poisson (
Stochastic calculus,
Point processes)
Dellacherie gave in
805 a proof by stochastic calculus of the previsible representation property for the Wiener and Poisson processes. A gap in this proof is filled in
928 for Brownian motion and here for Poisson processes
Keywords: Stochastic integrals,
Previsible representation,
Poisson processesNature: Correction Retrieve article from Numdam
XXII: 33, 449-453, LNM 1321 (1988)
LETTA, Giorgio
Un exemple de processus mesurable adapté non-progressif Retrieve article from Numdam
XXIII: 42, 531-535, LNM 1372 (1989)
LETTA, Giorgio
Sur les théorèmes de Hewitt-Savage et de de Finetti Retrieve article from Numdam
XXV: 26, 316-323, LNM 1485 (1991)
FUCHS, Aimé;
LETTA, Giorgio
Un résultat élémentaire de fiabilité. Application à la formule de Weierstrass sur la fonction gamma Retrieve article from Numdam
XL: 09, 203-225, LNM 1899 (2007)
CRIMALDI, Irene;
LETTA, Giorgio;
PRATELLI, Luca
A strong form of stable convergence
