6,497 research outputs found
A decomposition theorem for fuzzy set-valued random variables and a characterization of fuzzy random translation
Let be a fuzzy set--valued random variable (\frv{}), and \huku{X} the
family of all fuzzy sets for which the Hukuhara difference X\HukuDiff B
exists --almost surely. In this paper, we prove that can be
decomposed as X(\omega)=C\Mink Y(\omega) for --almost every
, is the unique deterministic fuzzy set that minimizes
as is varying in \huku{X}, and is a centered
\frv{} (i.e. its generalized Steiner point is the origin). This decomposition
allows us to characterize all \frv{} translation (i.e. X(\omega) = M \Mink
\indicator{\xi(\omega)} for some deterministic fuzzy convex set and some
random element in \Banach). In particular, is an \frv{} translation if
and only if the Aumann expectation is equal to up to a
translation.
Examples, such as the Gaussian case, are provided.Comment: 12 pages, 1 figure. v2: minor revision. v3: minor revision;
references, affiliation and acknowledgments added. Submitted versio
A Note on Fuzzy Set--Valued Brownian Motion
In this paper, we prove that a fuzzy set--valued Brownian motion , as
defined in [1], can be handle by an --valued Wiener process , in the
sense that B_t =\indicator{b_t}; i.e. it is actually the indicator function
of a Wiener process
Representation of maxitive measures: an overview
Idempotent integration is an analogue of Lebesgue integration where
-maxitive measures replace -additive measures. In addition to
reviewing and unifying several Radon--Nikodym like theorems proven in the
literature for the idempotent integral, we also prove new results of the same
kind.Comment: 40 page
Some Conditional Correlation Inequalities for Percolation and Related Processes
Consider ordinary bond percolation on a finite or countably infinite graph.
Let s, t, a and b be vertices. An earlier paper proved the (nonintuitive)
result that, conditioned on the event that there is no open path from s to t,
the two events "there is an open path from s to a" and "there is an open path
from s to b" are positively correlated. In the present paper we further
investigate and generalize the theorem of which this result was a consequence.
This leads to results saying, informally, that, with the above conditioning,
the open cluster of s is conditionally positively (self-)associated and that it
is conditionally negatively correlated with the open cluster of t.
We also present analogues of some of our results for (a) random-cluster
measures, and (b) directed percolation and contact processes, and observe that
the latter lead to improvements of some of the results in a paper of Belitsky,
Ferrari, Konno and Liggett (1997)
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