[Forum SIS] Avviso seminrio

[barbara.vantaggi a sbai.uniroma1.it]

AVVISO SEMINARIO
Dipartimento S.B.A.I. Univ. La Sapienza Roma
Venerdi 11 maggio

ore 14.30 Aula 1B1 PROF. PIETRO RIGO (Univ. di Pavia)
Misure martingala equivalenti finitamente additive

Abstract: Let $L$ be a linear space of real bounded random variables on the
probability space $(\Omega,\mathcal{A},P_0)$. A finitely additive
probability $P$ on $\mathcal{A}$ such that
\begin{equation*}
P\sim P_0\quad\text{and}\quad E_P(X)=0\text{ for each }X\in L
\end{equation*}
is called EMFA (equivalent martingale finitely additive probability). Two
characterizations of EMFA's are discussed in this talk. Some results of
the following type are described as well. Let $y\in\mathbb{R}$ and $Y$ a
bounded random variable. Then $X_n+y\overset{a.s.}\longrightarrow Y$, for
some sequence $(X_n)\subset L$, provided EMFA's exist and $E_P(Y)=y$ for
each EMFA $P$. Special attention is devoted to the particular case where
$P_0$ is atomic. Finally, various examples are given.


ore 15.30  Aula 1B1 PROF.  PATRIZIA BERTI (Univ. Modena e Reggio Emilia)
Una legge dei grandi numeri considerata in Economia

Abstract: Let $\Gamma$ be a Borel probability measure on $\mathbb{R}$ and
$(T,\mathcal{C},Q)$ a nonatomic probability space. Define
$\mathcal{H}=\{H\in\mathcal{C}:Q(H)>0\}$. In some economic models, the
following condition is requested. There are a probability space
$(\Omega,\mathcal{A},P)$ and a real process $X=\{X_t:t\in T\}$ satisfying
\begin{gather*}
\text{for each }H\in\mathcal{H},\text{ there is
}A_H\in\mathcal{A}\text{ with }P(A_H)=1\text{ such that }
t\mapsto X(t,\omega)\text{ is measurable and
}\,Q\bigl(\{t:X(t,\omega)\in\cdot\}\mid H\bigr)=\Gamma(\cdot)\,\text{ for
}\omega\in A_H.
\end{gather*}
Such a condition fails if $P$ is countably additive, $\mathcal{C}$
countably generated and $\Gamma$ non trivial. Instead, as discussed in
this talk, it holds for any $\mathcal{C}$ and $\Gamma$ under a finitely
additive probability $P$. Also, $X$ can be taken to have any given
distribution.

Cordiali saluti
--
Barbara Vantaggi
Dip. S.B.A.I.
Universita' La Sapienza di Roma
via Scarpa 16, 00161 Roma