1,326 research outputs found
Small and Large Time Stability of the Time taken for a L\'evy Process to Cross Curved Boundaries
This paper is concerned with the small time behaviour of a L\'{e}vy process
. In particular, we investigate the {\it stabilities} of the times,
\Tstarb(r) and \Tbarb(r), at which , started with , first leaves
the space-time regions (one-sided exit),
or (two-sided exit), , as
r\dto 0. Thus essentially we determine whether or not these passage times
behave like deterministic functions in the sense of different modes of
convergence; specifically convergence in probability, almost surely and in
. In many instances these are seen to be equivalent to relative stability
of the process itself. The analogous large time problem is also discussed
A Hydraulic Approach to Equilibria of Resource Selection Games
Drawing intuition from a (physical) hydraulic system, we present a novel
framework, constructively showing the existence of a strong Nash equilibrium in
resource selection games (i.e., asymmetric singleton congestion games) with
nonatomic players, the coincidence of strong equilibria and Nash equilibria in
such games, and the uniqueness of the cost of each given resource across all
Nash equilibria. Our proofs allow for explicit calculation of Nash equilibrium
and for explicit and direct calculation of the resulting (unique) costs of
resources, and do not hinge on any fixed-point theorem, on the Minimax theorem
or any equivalent result, on linear programming, or on the existence of a
potential (though our analysis does provide powerful insights into the
potential, via a natural concrete physical interpretation). A generalization of
resource selection games, called resource selection games with I.D.-dependent
weighting, is defined, and the results are extended to this family, showing the
existence of strong equilibria, and showing that while resource costs are no
longer unique across Nash equilibria in games of this family, they are
nonetheless unique across all strong Nash equilibria, drawing a novel
fundamental connection between group deviation and I.D.-congestion. A natural
application of the resulting machinery to a large class of
constraint-satisfaction problems is also described.Comment: Hebrew University of Jerusalem Center for the Study of Rationality
discussion paper 67
Testing for monotone increasing hazard rate
A test of the null hypothesis that a hazard rate is monotone nondecreasing,
versus the alternative that it is not, is proposed. Both the test statistic and
the means of calibrating it are new. Unlike previous approaches, neither is
based on the assumption that the null distribution is exponential. Instead,
empirical information is used to effectively identify and eliminate from
further consideration parts of the line where the hazard rate is clearly
increasing; and to confine subsequent attention only to those parts that
remain. This produces a test with greater apparent power, without the excessive
conservatism of exponential-based tests. Our approach to calibration borrows
from ideas used in certain tests for unimodality of a density, in that a
bandwidth is increased until a distribution with the desired properties is
obtained. However, the test statistic does not involve any smoothing, and is,
in fact, based directly on an assessment of convexity of the distribution
function, using the conventional empirical distribution. The test is shown to
have optimal power properties in difficult cases, where it is called upon to
detect a small departure, in the form of a bump, from monotonicity. More
general theoretical properties of the test and its numerical performance are
explored.Comment: Published at http://dx.doi.org/10.1214/009053605000000039 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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