Excursions of the integral of the Brownian motion
نویسنده
چکیده
The integrated Brownian motion is sometimes known as the Langevin process. Lachal studied several excursion laws induced by the latter. Here we follow a different point of view developed by Pitman for general stationary processes. We first construct a stationary Langevin process and then determine explicitly its stationary excursion measure. This is then used to provide new descriptions of Itô’s excursion measure of the Langevin process reflected at a completely inelastic boundary, which has been introduced recently by Bertoin. Résumé L’intégrale du mouvement Brownien est parfois appelée processus de Langevin. Lachal a étudié plusieurs lois d’excursions qui lui sont associées. Nous suivons ici un point de vue différent, développé par Pitman, pour les processus stationnaires. Nous construisons d’abord un processus de Langevin stationnaire avant d’en déterminer explicitement la mesure d’excursion stationnaire. Ce travail permet alors de fournir une nouvelle description de la mesure d’excursion d’Itô du processus de Langevin réfléchi sur une barrière inélastique, introduit récemment par Bertoin.
منابع مشابه
Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion
متن کامل
A wavelet method for stochastic Volterra integral equations and its application to general stock model
In this article,we present a wavelet method for solving stochastic Volterra integral equations based on Haar wavelets. First, we approximate all functions involved in the problem by Haar Wavelets then, by substituting the obtained approximations in the problem, using the It^{o} integral formula and collocation points then, the main problem changes into a system of linear or nonlinear equation w...
متن کاملA computational wavelet method for numerical solution of stochastic Volterra-Fredholm integral equations
A Legendre wavelet method is presented for numerical solutions of stochastic Volterra-Fredholm integral equations. The main characteristic of the proposed method is that it reduces stochastic Volterra-Fredholm integral equations into a linear system of equations. Convergence and error analysis of the Legendre wavelets basis are investigated. The efficiency and accuracy of the proposed method wa...
متن کاملAPPROXIMATION SOLUTION OF TWO-DIMENSIONAL LINEAR STOCHASTIC FREDHOLM INTEGRAL EQUATION BY APPLYING THE HAAR WAVELET
In this paper, we introduce an efficient method based on Haar wavelet to approximate a solutionfor the two-dimensional linear stochastic Fredholm integral equation. We also give an example to demonstrate the accuracy of the method.
متن کاملBrownian excursions, stochastic integrals, and representation of Wiener functionals
A stochastic calculus similar to Malliavin’s calculus is worked out for Brownian excursions. The analogue of the Malliavin derivative in this calculus is not a differential operator, but its adjoint is (like the Skorohod integral) an extension of the Itô integral. As an application, we obtain an expression for the integrand in the stochastic integral representation of square integrable Wiener f...
متن کاملCFD simulations on natural convection heat transfer of alumina-water nanofluid with Brownian motion effect in a 3-D enclosure
The CFD simulation has been undertaken concerning natural convection heat transfer of a nanofluid in vertical square enclosure, whose dimension, width height length (mm), is 40 40 90, respectively. The nanofluid used in the present study is -water with various volumetric fractions of the alumina nanoparticles ranging from 0-3%. The Rayleigh number is . Fluent v6.3 is used to simulate nanofluid ...
متن کامل