413 research outputs found
Geometrically stopped Markovian random growth processes and Pareto tails
Many empirical studies document power law behavior in size distributions of
economic interest such as cities, firms, income, and wealth. One mechanism for
generating such behavior combines independent and identically distributed
Gaussian additive shocks to log-size with a geometric age distribution. We
generalize this mechanism by allowing the shocks to be non-Gaussian (but
light-tailed) and dependent upon a Markov state variable. Our main results
provide sharp bounds on tail probabilities, a simple equation determining
Pareto exponents, and comparative statics. We present two applications: we show
that (i) the tails of the wealth distribution in a heterogeneous-agent dynamic
general equilibrium model with idiosyncratic investment risk are Paretian, and
(ii) a random growth model for the population dynamics of Japanese
municipalities is consistent with the observed Pareto exponent but only after
allowing for Markovian dynamics
Rank-based estimation for all-pass time series models
An autoregressive-moving average model in which all roots of the
autoregressive polynomial are reciprocals of roots of the moving average
polynomial and vice versa is called an all-pass time series model. All-pass
models are useful for identifying and modeling noncausal and noninvertible
autoregressive-moving average processes. We establish asymptotic normality and
consistency for rank-based estimators of all-pass model parameters. The
estimators are obtained by minimizing the rank-based residual dispersion
function given by Jaeckel [Ann. Math. Statist. 43 (1972) 1449--1458]. These
estimators can have the same asymptotic efficiency as maximum likelihood
estimators and are robust. The behavior of the estimators for finite samples is
studied via simulation and rank estimation is used in the deconvolution of a
simulated water gun seismogram.Comment: Published at http://dx.doi.org/10.1214/009053606000001316 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Noninvertibility and non-Markovianity of quantum dynamical maps
We identify two broad types of noninvertibilities in quantum dynamical maps,
one necessarily associated with CP-indivisibility and one not so. Next, we
study the production of (non-)Markovian, invertible maps by the process of
mixing noninvertible Pauli maps. The memory kernel perspective appears to be
less transparent on the issue of invertibility than the approaches based on
maps or master equations. Here we consider a related and potentially helpful
issue: that of identifying criteria of parameterized families of maps leading
to the existence of a well-defined semigroup limit.Comment: 7 pages, 2 figure
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