9,884 research outputs found
Convergence of densities of some functionals of Gaussian processes
The aim of this paper is to establish the uniform convergence of the
densities of a sequence of random variables, which are functionals of an
underlying Gaussian process, to a normal density. Precise estimates for the
uniform distance are derived by using the techniques of Malliavin calculus,
combined with Stein's method for normal approximation. We need to assume some
non-degeneracy conditions. First, the study is focused on random variables in a
fixed Wiener chaos, and later, the results are extended to the uniform
convergence of the derivatives of the densities and to the case of random
vectors in some fixed chaos, which are uniformly non-degenerate in the sense of
Malliavin calculus. Explicit upper bounds for the uniform norm are obtained for
random variables in the second Wiener chaos, and an application to the
convergence of densities of the least square estimator for the drift parameter
in Ornstein-Uhlenbeck processes is discussed
Feynman--Kac formula for the heat equation driven by fractional noise with Hurst parameter
In this paper, a Feynman-Kac formula is established for stochastic partial
differential equation driven by Gaussian noise which is, with respect to time,
a fractional Brownian motion with Hurst parameter . To establish such a
formula, we introduce and study a nonlinear stochastic integral from the given
Gaussian noise. To show the Feynman--Kac integral exists, one still needs to
show the exponential integrability of nonlinear stochastic integral. Then, the
approach of approximation with techniques from Malliavin calculus is used to
show that the Feynman-Kac integral is the weak solution to the stochastic
partial differential equation.Comment: Published in at http://dx.doi.org/10.1214/11-AOP649 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Improving Routing Efficiency through Intermediate Target Based Geographic Routing
The greedy strategy of geographical routing may cause the local minimum
problem when there is a hole in the routing area. It depends on other
strategies such as perimeter routing to find a detour path, which can be long
and result in inefficiency of the routing protocol. In this paper, we propose a
new approach called Intermediate Target based Geographic Routing (ITGR) to
solve the long detour path problem. The basic idea is to use previous
experience to determine the destination areas that are shaded by the holes. The
novelty of the approach is that a single forwarding path can be used to
determine a shaded area that may cover many destination nodes. We design an
efficient method for the source to find out whether a destination node belongs
to a shaded area. The source then selects an intermediate node as the tentative
target and greedily forwards packets to it, which in turn forwards the packet
to the final destination by greedy routing. ITGR can combine multiple shaded
areas to improve the efficiency of representation and routing. We perform
simulations and demonstrate that ITGR significantly reduces the routing path
length, compared with existing geographic routing protocols
- …