155 research outputs found
On the harmonic measure of stable processes
Using three hypergeometric identities, we evaluate the harmonic measure of a
finite interval and of its complementary for a strictly stable real L{\'e}vy
process. This gives a simple and unified proof of several results in the
literature, old and recent. We also provide a full description of the
corresponding Green functions. As a by-product, we compute the hitting
probabilities of points and describe the non-negative harmonic functions for
the stable process killed outside a finite interval
Uniform shrinking and expansion under isotropic Brownian flows
We study some finite time transport properties of isotropic Brownian flows.
Under a certain nondegeneracy condition on the potential spectral measure, we
prove that uniform shrinking or expansion of balls under the flow over some
bounded time interval can happen with positive probability. We also provide a
control theorem for isotropic Brownian flows with drift. Finally, we apply the
above results to show that under the nondegeneracy condition the length of a
rectifiable curve evolving in an isotropic Brownian flow with strictly negative
top Lyapunov exponent converges to zero as with positive
probability
Associação entre características de desempenho de tilápia-do-nilo ao longo do período de cultivo.
O objetivo deste trabalho foi estimar as herdabilidades e a estrutura de correlações genéticas entre as características de desempenho de tilápia-do-nilo (Oreochromis niloticus) da linhagem GIFT, em diferentes estágios do ciclo de produção. As tilápias foram cultivadas em tanques - rede. Mediu-se ganho em peso diário total, peso vivo e ganho em peso diário, em quatro períodos, com intervalos de aproximadamente 30 dias. Foram realizadas análises unicaracter para as medidas, em todas as biometrias e, nas análises bicaracter, as medidas de mesma característica foram combinadas duas a duas e com o ganho em peso diário total. As estimações de herdabilidade variaram de 0,15 a 0,11 para peso vivo, 0,16 a 0,09 para ganho em peso diário e 0,17 a 0,12 para ganho em peso diário total, nas análises unicaracter. Os valores estimados de correlação genética para peso vivo e ganho em peso diário, associados ao ganho em peso diário total, variaram entre 0,37 a 0,98 e 0,74 a 0,8 respectivamente. A forte associação genética estimada entre peso vivo em biometrias intermediárias e ganho em peso diário total sugere que a seleção para velocidade de crescimento pode ser realizada de forma precoce
Upper estimate of martingale dimension for self-similar fractals
We study upper estimates of the martingale dimension of diffusion
processes associated with strong local Dirichlet forms. By applying a general
strategy to self-similar Dirichlet forms on self-similar fractals, we prove
that for natural diffusions on post-critically finite self-similar sets
and that is dominated by the spectral dimension for the Brownian motion
on Sierpinski carpets.Comment: 49 pages, 7 figures; minor revision with adding a referenc
Well-posedness of the transport equation by stochastic perturbation
We consider the linear transport equation with a globally Holder continuous
and bounded vector field. While this deterministic PDE may not be well-posed,
we prove that a multiplicative stochastic perturbation of Brownian type is
enough to render the equation well-posed. This seems to be the first explicit
example of partial differential equation that become well-posed under the
influece of noise. The key tool is a differentiable stochastic flow constructed
and analysed by means of a special transformation of the drift of Ito-Tanaka
type.Comment: Addition of new part
Path Integrals on a Compact Manifold with Non-negative Curvature
A typical path integral on a manifold, is an informal expression of the
form \frac{1}{Z}\int_{\sigma \in H(M)} f(\sigma)
e^{-E(\sigma)}\mathcal{D}\sigma, \nonumber where is a Hilbert manifold
of paths with energy , is a real valued function on
, is a \textquotedblleft Lebesgue measure
\textquotedblright and is a normalization constant. For a compact
Riemannian manifold , we wish to interpret as a
Riemannian \textquotedblleft volume form \textquotedblright over ,
equipped with its natural metric. Given an equally spaced partition,
of let H_{{\mathcal{P}}%}(M) be the finite
dimensional Riemannian submanifold of consisting of piecewise geodesic
paths adapted to Under certain curvature restrictions on it
is shown that where is a \textquotedblleft
normalization\textquotedblright constant, is the
energy functional, Vol_{H_{{\mathcal{P}}%}} is the Riemannian volume measure
on is Wiener measure on continuous paths in
and is a certain density determined by the curvature tensor of $M.
Probabilistic Methods for the Incompressible Navier–Stokes Equations With Space Periodic Conditions
Two refreshing views of Fluctuation Theorems through Kinematics Elements and Exponential Martingale
In the context of Markov evolution, we present two original approaches to
obtain Generalized Fluctuation-Dissipation Theorems (GFDT), by using the
language of stochastic derivatives and by using a family of exponential
martingales functionals. We show that GFDT are perturbative versions of
relations verified by these exponential martingales. Along the way, we prove
GFDT and Fluctuation Relations (FR) for general Markov processes, beyond the
usual proof for diffusion and pure jump processes. Finally, we relate the FR to
a family of backward and forward exponential martingales.Comment: 41 pages, 7 figures; version2: 45 pages, 7 figures, minor revisions,
new results in Section
Feynman-Kac equation for anomalous processes with space-and time-dependent forces
Invited contribution to the J. Phys. A special issue Emerging Talent
Time separation as a hidden variable to the Copenhagen school of quantum mechanics
The Bohr radius is a space-like separation between the proton and electron in
the hydrogen atom. According to the Copenhagen school of quantum mechanics, the
proton is sitting in the absolute Lorentz frame. If this hydrogen atom is
observed from a different Lorentz frame, there is a time-like separation
linearly mixed with the Bohr radius. Indeed, the time-separation is one of the
essential variables in high-energy hadronic physics where the hadron is a bound
state of the quarks, while thoroughly hidden in the present form of quantum
mechanics. It will be concluded that this variable is hidden in Feynman's rest
of the universe. It is noted first that Feynman's Lorentz-invariant
differential equation for the bound-state quarks has a set of solutions which
describe all essential features of hadronic physics. These solutions explicitly
depend on the time separation between the quarks. This set also forms the
mathematical basis for two-mode squeezed states in quantum optics, where both
photons are observable, but one of them can be treated a variable hidden in the
rest of the universe. The physics of this two-mode state can then be translated
into the time-separation variable in the quark model. As in the case of the
un-observed photon, the hidden time-separation variable manifests itself as an
increase in entropy and uncertainty.Comment: LaTex 10 pages with 5 figure. Invited paper presented at the
Conference on Advances in Quantum Theory (Vaxjo, Sweden, June 2010), to be
published in one of the AIP Conference Proceedings serie
- …