[图书][B] Optimization and nonstandard analysis
JE Rubio - 1994 - books.google.com
This text presents an up-to-date overview of optimization and control theory, including
existence theory, modelling, approximation and numerical methods. It also provides a self …
existence theory, modelling, approximation and numerical methods. It also provides a self …
[图书][B] Hypermodels in mathematical finance: Modelling via infinitesimal analysis
SA Ng - 2003 - books.google.com
At the beginning of the new millennium, two unstoppable processes are taking place in the
world:(1) globalization of the economy;(2) information revolution. As a consequence, there is …
world:(1) globalization of the economy;(2) information revolution. As a consequence, there is …
Loeb measure theory
N Cutland - Developments in nonstandard mathematics, 2020 - taylorfrancis.com
Loeb measures, discovered by Peter Loeb in 1975, are very rich yet tractable measure
spaces, which play a central and powerful role in many applications of nonstandard analysis …
spaces, which play a central and powerful role in many applications of nonstandard analysis …
Finitely-additive, countably-additive and internal probability measures
H Duanmu, W Weiss - arXiv preprint arXiv:2010.02463, 2020 - arxiv.org
We discuss two ways to construct standard probability measures, called push-down
measures, from internal probability measures. We show that the Wasserstein distance …
measures, from internal probability measures. We show that the Wasserstein distance …
[图书][B] Nonstandard methods in functional analysis: lectures and notes
SA Ng - 2010 - books.google.com
In the early 1960s, by using techniques from the model theory of first-order logic, Robinson
gave a rigorous formulation and extension of Leibniz'infinitesimal calculus. Since then, the …
gave a rigorous formulation and extension of Leibniz'infinitesimal calculus. Since then, the …
Borel measure extensions of measures defined on sub-σ-algebras
JM Aldaz, H Render - Advances in Mathematics, 2000 - Elsevier
We develop a new approach to the measure extension problem, based on nonstandard
analysis. The class of thick topological spaces, which includes all locally compact and all K …
analysis. The class of thick topological spaces, which includes all locally compact and all K …
Existence of matching priors on compact spaces
A matching prior at level is a prior such that an associated credible region is also a
confidence set. We study the existence of matching priors for general families of credible …
confidence set. We study the existence of matching priors for general families of credible …
The optimal control of nonlinear diffusion equations with rough initial data
JE Rubio - Journal of the Franklin Institute, 2000 - Elsevier
We consider in this paper a problem consisting of the optimal boundary control of a
nonlinear diffusion equation with a “rough” initial condition, that is, in which the initial …
nonlinear diffusion equation with a “rough” initial condition, that is, in which the initial …
[PDF][PDF] Countably determined sets and a conjecture of CW Henson
H Render - Mathematische Annalen, 1995 - academia.edu
It is well-known that descriptive set theory has many important applications to analysis, see
eg [9, 10]. In particular the notion of an analytic set, introduced in 1917 by M. Souslin, is of …
eg [9, 10]. In particular the notion of an analytic set, introduced in 1917 by M. Souslin, is of …
Pushing down infinite Loeb measures
DA Ross - Mathematica Scandinavica, 2009 - JSTOR
PUSHING DOWN INFINITE LOEB MEASURES Page 1 MATH. SC AND. 104 (2009), 108-116
PUSHING DOWN INFINITE LOEB MEASURES DAVID Α. ROSS Abstract Sufficient conditions …
PUSHING DOWN INFINITE LOEB MEASURES DAVID Α. ROSS Abstract Sufficient conditions …