On quadratic functionals of the Brownian sheet and related processes
نویسندگان
چکیده
Motivated by asymptotic problems in the theory of empirical processes, and specifically by tests of independence, we study the law of quadratic functionals of the (weighted) Brownian sheet and of the bivariate Brownian bridge on [0, 1]. In particular: (i) we use Fubini type techniques to establish identities in law with quadratic functionals of other Gaussian processes, (ii) we explicitly calculate the Laplace transform of such functionals by means of Karhunen-Loève expansions, (iii) we prove central and non-central limit theorems in the same spirit of Peccati and Yor (2004) and Nualart and Peccati (2004). Our results extend some classical computations due to P. Lévy (1950), as well as the formulae recently obtained by Deheuvels and Martynov (2003). AMS 2000 classification: 60F05; 60F15; 60G15; 60H07; 62G30
منابع مشابه
Effects of Brownian motion and Thermophoresis on MHD Mixed Convection Stagnation-point Flow of a Nanofluid Toward a Stretching Vertical Sheet in Porous Medium
This article deals with the study of the two-dimensional mixed convection magnetohydrodynamic (MHD) boundary layer of stagnation-point flow over a stretching vertical plate in porous medium filled with a nanofluid. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis in the presence of thermal radiation. The skin-friction coefficient, Nusselt number an...
متن کاملOn Symmetric Stable Random Variables and Matrix Transposition
In a companion paper, the authors obtained some Fubini type identities in law for quadratic functionals of Brownian motion, and, more generally, for certain functionals of symmetric stable processes, the function: x -* x2 then being replaced by: x e IxIa. In this paper, discrete analogues of such identities in law, which involve a sequence of independent standard symmetric stable r.v.'s of inde...
متن کاملUnsteady Hydromagnetic Flow of Eyring-Powell Nanofluid over an Inclined Permeable Stretching Sheet with Joule Heating and Thermal Radiation
The present analysis deals with an unsteady magnetohydrodynamic flow of Eyring-Powell nanofluid over an inclined permeable stretching sheet. Effects of thermal radiation, Joule heating, and chemical reaction are considered. The effects of Brownian motion and thermophoresis on the flow over the permeable stretching sheet are discussed. Using Runge-Kutta fourth-order along with shooting technique...
متن کاملExponential functionals of Brownian motion, II: Some related diffusion processes
This is the second part of our survey on exponential functionals of Brownian motion. We focus on the applications of the results about the distributions of the exponential functionals, which have been discussed in the first part. Pricing formula for call options for the Asian options, explicit expressions for the heat kernels on hyperbolic spaces, diffusion processes in random environments and ...
متن کاملBrownian Limits, Local Limits and Variance Asymptotics for Convex Hulls in the Ball by Pierre Calka,
Schreiber and Yukich [Ann. Probab. 36 (2008) 363–396] establish an asymptotic representation for random convex polytope geometry in the unit ball Bd , d ≥ 2, in terms of the general theory of stabilizing functionals of Poisson point processes as well as in terms of generalized paraboloid growth processes. This paper further exploits this connection, introducing also a dual object termed the par...
متن کامل