Search results for "approximation"

Estimation of total electricity consumption curves by sampling in a finite population when some trajectories are partially unobserved

2019

International audience; Millions of smart meters that are able to collect individual load curves, that is, electricity consumption time series, of residential and business customers at fine scale time grids are now deployed by electricity companies all around the world. It may be complex and costly to transmit and exploit such a large quantity of information, therefore it can be relevant to use survey sampling techniques to estimate mean load curves of specific groups of customers. Data collection, like every mass process, may undergo technical problems at every point of the metering and collection chain resulting in missing values. We consider imputation approaches (linear interpolation, k…

Random walk approximation of BSDEs with H{\"o}lder continuous terminal condition

2018

In this paper, we consider the random walk approximation of the solution of a Markovian BSDE whose terminal condition is a locally Hölder continuous function of the Brownian motion. We state the rate of the L2-convergence of the approximated solution to the true one. The proof relies in part on growth and smoothness properties of the solution u of the associated PDE. Here we improve existing results by showing some properties of the second derivative of u in space. peerReviewed

Lévy processes in bounded domains: path-wise reflection scenarios and signatures of confinement

2022

We discuss an impact of various (path-wise) reflection-from-the barrier scenarios upon confining properties of a paradigmatic family of symmetric $\alpha $-stable L\'{e}vy processes, whose permanent residence in a finite interval on a line is secured by a two-sided reflection. Depending on the specific reflection "mechanism", the inferred jump-type processes differ in their spectral and statistical characteristics, like e.g. relaxation properties, and functional shapes of invariant (equilibrium, or asymptotic near-equilibrium) probability density functions in the interval. The analysis is carried out in conjunction with attempts to give meaning to the notion of a reflecting L\'{e}vy process…

Adaptive sparse representation of continuous input for tsetlin machines based on stochastic searching on the line

2021

This paper introduces a novel approach to representing continuous inputs in Tsetlin Machines (TMs). Instead of using one Tsetlin Automaton (TA) for every unique threshold found when Booleanizing continuous input, we employ two Stochastic Searching on the Line (SSL) automata to learn discriminative lower and upper bounds. The two resulting Boolean features are adapted to the rest of the clause by equipping each clause with its own team of SSLs, which update the bounds during the learning process. Two standard TAs finally decide whether to include the resulting features as part of the clause. In this way, only four automata altogether represent one continuous feature (instead of potentially h…

European Option Pricing and Hedging with Both Fixed and Proportional Transaction Costs

2003

Abstract In this paper we provide a systematic treatment of the utility based option pricing and hedging approach in markets with both fixed and proportional transaction costs: we extend the framework developed by Davis et al. (SIAM J. Control Optim., 31 (1993) 470) and formulate the option pricing and hedging problem. We propose and implement a numerical procedure for computing option prices and corresponding optimal hedging strategies. We present a careful analysis of the optimal hedging strategy and elaborate on important differences between the exact hedging strategy and the asymptotic hedging strategy of Whalley and Wilmott (RISK 7 (1994) 82). We provide a simulation analysis in order …

On Malliavin calculus and approximation of stochastic integrals for Lévy processes

2012

Adaptive Wavelet Methods for SPDEs

2014

We review a series of results that have been obtained in the context of the DFG-SPP 1324 project “Adaptive wavelet methods for SPDEs”. This project has been concerned with the construction and analysis of adaptive wavelet methods for second order parabolic stochastic partial differential equations on bounded, possibly nonsmooth domains \(\mathcal{O}\subset \mathbb{R}^{d}\). A detailed regularity analysis for the solution process u in the scale of Besov spaces \(B_{\tau,\tau }^{s}(\mathcal{O})\), 1∕τ = s∕d + 1∕p, α > 0, p ≥ 2, is presented. The regularity in this scale is known to determine the order of convergence that can be achieved by adaptive wavelet algorithms and other nonlinear appro…

Linear and nonlinear approximations for periodically driven bistable systems

2005

We analyze periodically driven bistable systems by two different approaches. The first approach is a linearization of the stochastic Langevin equation of our system by the response on small external force. The second one is based on the Gaussian approximation of the kinetic equations for the cumulants. We obtain with the first approach the signal power amplification and output signal-to-noise ratio for a model piece-wise linear bistable potential and compare with the results of linear response approximation. By using the second approach to a bistable quartic potential, we obtain the set of nonlinear differential equations for the first and the second cumulants.

Electronic Properties, Band Structure, and Fermi Surface Instabilities ofNi1+/Ni2+NickelateLa3Ni2O6, Isoelectronic with Superconducting Cuprates

2009

Electronic structure calculations were performed for the mixed-valent Ni(1+)/Ni(2+) nickelate La3Ni2O6, which exhibits electronic instabilities of the Fermi surface similar to that of the isostructural superconducting La2CaCu2O6 cuprate. La3Ni2O6 shows activated hopping, which fits to Mott's variable-range-hopping model with localized states near the Fermi level. However, a simple local spin density approximation calculation leads to a metallic ground state. The calculations including local density approximation+Hubbard U and hybrid functionals indicate a multiply degenerate magnetic ground state. For electron-doped La2ZrNi2O6, which is isoelectronic with La2CaCu2O6, an antiferromagnetic in…

Unified description of 2+_1 states within the deformed quasiparticle random-phase approximation

2013

We describe low-lying collective states in deformed even-even nuclei within a deformed quasiparticle random-phase approximation (dQRPA) by using a single-particle basis with good angular momentum. The statistical factors, accounting for the level occupancy, appear in the dQRPA in a natural way as rotation coefficients that take the intrinsic system to the laboratory system. We have used our model by performing a systematic analysis of E2 transitions from the first ${2}^{+}$ state to the ground state for all superfluid nuclei in the range $50lZ\ensuremath{\le}100$ by using a common charge polarization parameter $\ensuremath{\chi}=0.2$. In spite of its similarity to the QRPA, this method is a…