Search results for "Numerical"
showing 10 items of 2002 documents
CALIBRATION OF LÉVY PROCESSES USING OPTIMAL CONTROL OF KOLMOGOROV EQUATIONS WITH PERIODIC BOUNDARY CONDITIONS
2018
We present an optimal control approach to the problem of model calibration for L\'evy processes based on a non parametric estimation procedure. The calibration problem is of considerable interest in mathematical finance and beyond. Calibration of L\'evy processes is particularly challenging as the jump distribution is given by an arbitrary L\'evy measure, which form a infinite dimensional space. In this work, we follow an approach which is related to the maximum likelihood theory of sieves. The sampling of the L\'evy process is modelled as independent observations of the stochastic process at some terminal time $T$. We use a generic spline discretization of the L\'evy jump measure and selec…
Numerical construction of the density-potential mapping
2018
We demonstrate how a recently developed method Nielsen et al. [Nielsen et al., EPL 101, 33001 (2013)] allows for a comprehensive investigation of time-dependent density functionals in general, and of the exact time-dependent exchange-correlation potential in particular, by presenting the first exact results for two- and three-dimensional multi-electron systems. This method is an explicit realization of the Runge–Gross correspondence, which maps time-dependent densities to their respective potentials, and allows for the exact construction of desired density functionals. We present in detail the numerical requirements that makes this method efficient, stable and precise even for large and rap…
Numerical methods for pricing options under jump-diffusion processes
2013
An introductive course to some numerical approximation methods for ordinary and partial differential equations
2021
These lectures notes were written for students of the first year of the international Master ‘Maths for Physics’ at the University of Burgundy in 2021, as a part of the course called ‘Numerical Methods’. It was designed for a total of 22 hours of classes. The main objective of this course is to provide a first insight into numerical methods to solve mathematical problems inspired from physics and engineering. It focuses both on the mathematical fundations and justifications of numerical methods and on practical aspects related to their implementation.
Semantic Complexity in Natural Language
2015
This chapter presents the technical framework that the authors used to define fragments of natural languages and formulate questions as to their semantic complexity. It examines the study of the classical syllogistic and its extensions. It analyzes the semantic complexity of various salient fragments of English. It highlights that the language of argument, featuring transitive verbs, is in an objective sense inferentially no more complex than the language of classical syllogisms exemplified by argument, indeed, the analogous extension featuring ditransitive verbs involves only a modest increase in complexity. On the other hand, the language of argument, which adds relative clauses to the cl…
Numerical expressions in everyday language
2016
This interesting volume was published by the Laterza in 2011 and is the product of fruitful collaboration between three internationally renowned scholars, each with different research perspectives. They are respectively Carla Bazzanella, who teaches General and Cognitive Linguistics at the University of Turin; Rosa Pugliese, who teaches Italian as a foreign language at the University of Bologna; Erdling Strudsholm, who teaches Italian linguistics at the University of Copenhagen.
Numerical Magnitude Affects Accuracy but Not Precision of Temporal Judgments
2021
A Theory of Magnitude (ATOM) suggests that space, time, and quantities are processed through a generalized magnitude system. ATOM posits that task-irrelevant magnitudes interfere with the processing of task-relevant magnitudes as all the magnitudes are processed by a common system. Many behavioral and neuroimaging studies have found support in favor of a common magnitude processing system. However, it is largely unknown whether such cross-domain monotonic mapping arises from a change in the accuracy of the magnitude judgments or results from changes in precision of the processing of magnitude. Therefore, in the present study, we examined whether large numerical magnitude affects temporal ac…
A review of the analytical and numerical modeling of composites
2016
This review article is dedicated to the materials that are made from two or more constituent materials with different physical and/or chemical properties. The focus is on the materials, where the individual components remain separate and distinct within the final structure. The new combined material usually have some additional characteristic properties compared to the individual components, or, in other case, some critical properties of combined material may follow almost equally one of the components. Typically, preferred properties of the new material can be such as strength, porosity, conductivity or cheapness. The ultimate goal of this study is to find methods and tools for achieve adequ…