1,078 research outputs found
On Sampling of stationary increment processes
Under a complex technical condition, similar to such used in extreme value
theory, we find the rate q(\epsilon)^{-1} at which a stochastic process with
stationary increments \xi should be sampled, for the sampled process
\xi(\lfloor\cdot /q(\epsilon)\rfloor q(\epsilon)) to deviate from \xi by at
most \epsilon, with a given probability, asymptotically as \epsilon
\downarrow0. The canonical application is to discretization errors in computer
simulation of stochastic processes.Comment: Published at http://dx.doi.org/10.1214/105051604000000468 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
On overload in a storage model, with a self-similar and infinitely divisible input
Let {X(t)}_{t\ge0} be a locally bounded and infinitely divisible stochastic
process, with no Gaussian component, that is self-similar with index H>0.
Pick constants \gamma >H and c>0. Let \nu be the L\'evy measure on
R^{[0,\infty)} of X, and suppose that R(u)\equiv\nu({y\inR^{[0,\infty)}:supt\ge
0y(t)/(1+ct^{\gamma})>u}) is suitably ``heavy tailed'' as u\to\infty (e.g.,
subexponential with positive decrease). For the ``storage process'' Y(t)\equiv
sup_{s\ge t}(X(s)-X(t)-c(s-t)^{\gamma}), we show that
P{sup_{s\in[0,t(u)]}Y(s)>u}\sim P{Y(\hat t(u))>u} as u\to\infty, when 0\le \hat
t(u)\le t(u) do not grow too fast with u [e.g., t(u)=o(u^{1/\gamma})]
A note on a gauge-gravity relation and functional determinants
We present a refinement of a recently found gauge-gravity relation between
one-loop effective actions: on the gauge side, for a massive charged scalar in
2d dimensions in a constant maximally symmetric electromagnetic field; on the
gravity side, for a massive spinor in d-dimensional (Euclidean) anti-de Sitter
space. The inclusion of the dimensionally regularized volume of AdS leads to
complete mapping within dimensional regularization. In even-dimensional AdS, we
get a small correction to the original proposal; whereas in odd-dimensional
AdS, the mapping is totally new and subtle, with the `holographic trace
anomaly' playing a crucial role.Comment: 6 pages, io
Inverse problem by Cauchy data on arbitrary subboundary for system of elliptic equations
We consider an inverse problem of determining coefficient matrices in an
-system of second-order elliptic equations in a bounded two dimensional
domain by a set of Cauchy data on arbitrary subboundary. The main result of the
article is as follows: If two systems of elliptic operators generate the same
set of partial Cauchy data on an arbitrary subboundary, then the coefficient
matrices of the first-order and zero-order terms satisfy the prescribed system
of first-order partial differential equations. The main result implies the
uniqueness of any two coefficient matrices provided that the one remaining
matrix among the three coefficient matrices is known
Identificação de atividade antiinflamatória em plantas do horto da Embrapa Amazônia Oriental.
On the infimum attained by a reflected L\'evy process
This paper considers a L\'evy-driven queue (i.e., a L\'evy process reflected
at 0), and focuses on the distribution of , that is, the minimal value
attained in an interval of length (where it is assumed that the queue is in
stationarity at the beginning of the interval). The first contribution is an
explicit characterization of this distribution, in terms of Laplace transforms,
for spectrally one-sided L\'evy processes (i.e., either only positive jumps or
only negative jumps). The second contribution concerns the asymptotics of
\prob{M(T_u)> u} (for different classes of functions and large);
here we have to distinguish between heavy-tailed and light-tailed scenarios
Partition functions and double-trace deformations in AdS/CFT
We study the effect of a relevant double-trace deformation on the partition
function (and conformal anomaly) of a CFT at large N and its dual picture in
AdS. Three complementary previous results are brought into full agreement with
each other: bulk and boundary computations, as well as their formal identity.
We show the exact equality between the dimensionally regularized partition
functions or, equivalently, fluctuational determinants involved. A series of
results then follows: (i) equality between the renormalized partition functions
for all d; (ii) for all even d, correction to the conformal anomaly; (iii) for
even d, the mapping entails a mixing of UV and IR effects on the same side
(bulk) of the duality, with no precedent in the leading order computations; and
finally, (iv) a subtle relation between overall coefficients, volume
renormalization and IR-UV connection. All in all, we get a clean test of the
AdS/CFT correspondence beyond the classical SUGRA approximation in the bulk and
at subleading O(1) order in the large-N expansion on the boundary.Comment: 18 pages, uses JHEP3.cls. Published JHEP versio
‘I felt uncomfortable because I know what it can be’: The emotional geographies and implicit activisms of reflexive practices for early childhood teachers
Implied volatility of basket options at extreme strikes
In the paper, we characterize the asymptotic behavior of the implied
volatility of a basket call option at large and small strikes in a variety of
settings with increasing generality. First, we obtain an asymptotic formula
with an error bound for the left wing of the implied volatility, under the
assumption that the dynamics of asset prices are described by the
multidimensional Black-Scholes model. Next, we find the leading term of
asymptotics of the implied volatility in the case where the asset prices follow
the multidimensional Black-Scholes model with time change by an independent
increasing stochastic process. Finally, we deal with a general situation in
which the dependence between the assets is described by a given copula
function. In this setting, we obtain a model-free tail-wing formula that links
the implied volatility to a special characteristic of the copula called the
weak lower tail dependence function
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