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We consider the problem of nonparametric estimation of the drift and diffusion coefficients of a Stochastic Differential Equation (SDE), based on n independent replicates {Xi(t) : t is an element of [0 , 1]}13 d B(t), where alpha is an element of {0 , 1} a ...
We consider processes which have the distribution of standard Brownian motion (in the forward direction of time) starting from random points on the trajectory which accumulate at -∞ 1. We show that these processes do not have to have the distribution of st ...
Among the rich collection of noise sources that can be used to drive stochastic differential equations (SDE), we here focus on Markov processes that themselves are functions of the standard Brownian motion and of the Telegrapher’s process. Our present nois ...
This article derives a closed-form pricing formula for European exchange options under a non-Gaussianframework for the underlying assets, intending to resolve mispricing associated with a geometric Brownianmotion. The dynamics of each of the two correlated ...
We develop a doubly spectral representation of a stationary functional time series, and study the properties of its empirical version. The representation decomposes the time series into an integral of uncorrelated frequency components (Cramer representatio ...
This work is about time series of functional data (functional time series), and consists of three main parts. In the first part (Chapter 2), we develop a doubly spectral decomposition for functional time series that generalizes the Karhunen–Loève expansion ...
We introduce an extended class of cardinal LL-splines, where L is a pseudo-differential operator satisfying some admissibility conditions. We show that the LL-spline signal interpolation problem is well posed and that its solution is the unique minimizer ...
Abstract We study the diamagnetic surface currents of particles in thermal equilibrium submitted to a constant magnetic field. The current density of independent electrons with Boltzmann (respectively Fermi) statistics has a gaussian (respectively exponent ...
