3,905 research outputs found
Thou shalt not say "at random" in vain: Bertrand's paradox exposed
We review the well known Bertrand paradoxes, and we first maintain that they
do not point to any probabilistic inconsistency, but rather to the risks
incurred with a careless use of the locution "at random". We claim then that
these paradoxes spring up also in the discussion of the celebrated Buffon's
needle problem, and that they are essentially related to the definition of
(geometrical) probabilities on "uncountably" infinite sets. A few empirical
remarks are finally added to underline the difference between "passive" and
"active" randomness, and the prospects of any experimental decisionComment: 17 pages, 4 figures. Added: Appendix A; References 7, 8, 10;
Modified: Abstract; Section 4; a few sentences elsewher
A semi-Markov model with memory for price changes
We study the high frequency price dynamics of traded stocks by a model of
returns using a semi-Markov approach. More precisely we assume that the
intraday returns are described by a discrete time homogeneous semi-Markov which
depends also on a memory index. The index is introduced to take into account
periods of high and low volatility in the market. First of all we derive the
equations governing the process and then theoretical results have been compared
with empirical findings from real data. In particular we analyzed high
frequency data from the Italian stock market from first of January 2007 until
end of December 2010
Selfdecomposability and selfsimilarity: a concise primer
We summarize the relations among three classes of laws: infinitely divisible,
selfdecomposable and stable. First we look at them as the solutions of the
Central Limit Problem; then their role is scrutinized in relation to the Levy
and the additive processes with an emphasis on stationarity and selfsimilarity.
Finally we analyze the Ornstein-Uhlenbeck processes driven by Levy noises and
their selfdecomposable stationary distributions, and we end with a few
particular examples.Comment: 24 pages, 3 figures; corrected misprint in the title; redactional
modifications required by the referee; added references from [16] to [28];.
Accepted and in press on Physica
Controlled quantum evolutions and transitions
We study the nonstationary solutions of Fokker-Planck equations associated to
either stationary or nonstationary quantum states. In particular we discuss the
stationary states of quantum systems with singular velocity fields. We
introduce a technique that allows to realize arbitrary evolutions ruled by
these equations, to account for controlled quantum transitions. The method is
illustrated by presenting the detailed treatment of the transition
probabilities and of the controlling time-dependent potentials associated to
the transitions between the stationary, the coherent, and the squeezed states
of the harmonic oscillator. Possible extensions to anharmonic systems and mixed
states are briefly discussed and assessed.Comment: 24 pages, 4 figure
A semi-Markov model for price returns
We study the high frequency price dynamics of traded stocks by a model of
returns using a semi-Markov approach. More precisely we assume that the
intraday return are described by a discrete time homogeneous semi-Markov
process and the overnight returns are modeled by a Markov chain. Based on this
assumptions we derived the equations for the first passage time distribution
and the volatility autocorreletion function. Theoretical results have been
compared with empirical findings from real data. In particular we analyzed high
frequency data from the Italian stock market from first of January 2007 until
end of December 2010. The semi-Markov hypothesis is also tested through a
nonparametric test of hypothesis
Measures of lexical distance between languages
The idea of measuring distance between languages seems to have its roots in
the work of the French explorer Dumont D'Urville \cite{Urv}. He collected
comparative words lists of various languages during his voyages aboard the
Astrolabe from 1826 to 1829 and, in his work about the geographical division of
the Pacific, he proposed a method to measure the degree of relation among
languages. The method used by modern glottochronology, developed by Morris
Swadesh in the 1950s, measures distances from the percentage of shared
cognates, which are words with a common historical origin. Recently, we
proposed a new automated method which uses normalized Levenshtein distance
among words with the same meaning and averages on the words contained in a
list. Recently another group of scholars \cite{Bak, Hol} proposed a refined of
our definition including a second normalization. In this paper we compare the
information content of our definition with the refined version in order to
decide which of the two can be applied with greater success to resolve
relationships among languages
Spot foreign exchange market and time series
We investigate high frequency price dynamics in foreign exchange market using
data from Reuters information system (the dataset has been provided to us by
Ols en & Associates). In our analysis we show that a na\"ive approach to the
definition of price (for example using the spot midprice) may lead to wrong
conclusions on price behavior as for example the presence of short term
covariances for returns.
For this purpose we introduce an algorithm which only uses the non arbitrage
principle to estimate real prices from the spot ones. The new definition leads
to returns which are i.i.d. variables and therefore are not affected by
spurious correlations. Furthermore, any apparent information (defined by using
Shannon entropy) contained in the data disappears
Indo-European languages tree by Levenshtein distance
The evolution of languages closely resembles the evolution of haploid
organisms. This similarity has been recently exploited \cite{GA,GJ} to
construct language trees. The key point is the definition of a distance among
all pairs of languages which is the analogous of a genetic distance. Many
methods have been proposed to define these distances, one of this, used by
glottochronology, compute distance from the percentage of shared ``cognates''.
Cognates are words inferred to have a common historical origin, and subjective
judgment plays a relevant role in the identification process. Here we push
closer the analogy with evolutionary biology and we introduce a genetic
distance among language pairs by considering a renormalized Levenshtein
distance among words with same meaning and averaging on all the words contained
in a Swadesh list \cite{Sw}. The subjectivity of process is consistently
reduced and the reproducibility is highly facilitated. We test our method
against the Indo-European group considering fifty different languages and the
two hundred words of the Swadesh list for any of them. We find out a tree which
closely resembles the one published in \cite{GA} with some significant
differences
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