© University of Kent - Contact | Feedback | Legal | FOI | Cookies
Constructive potential theory: A linear logic approach
Marius Constantin Bujorianu and Manuela Luminita Bujorianu
In A. Berarducci and N.J. Cutland, editors, NS 2002 Non-standard Methods and Applications in Mathematics, pages 182-196, Pisa, Italy, June 2002. AMS-UMI, University of Pisa Mini-symposion "Reuniting the Antipodes II: Constructive and Nonstandard Views of the Continuum".Abstract
In this paper we propose a constructive and logical foundation of stochastic analysis (more precise its axiomatic heart, axiomatic potential theory) using Abrusci's weak-commutative linear logic and Wiklicky's Hilbert Machine quantitative computational model. A general process algebra, named continuous process algebra or continuous information processing systems has been developed. An important application of this process algebra is that we can associate to each Hilbert machine a Dirichlet space, providing in this way a logical and computational model to each class of applications of Dirichlet spaces. We study the possible applications of this refined model to a large diversity of applied mathematics (including financial mathematics, stochastic processes and mathematical physics) via Dirichlet spaces.
Bibtex Record
@inproceedings{1525,
author = {Marius Constantin Bujorianu and Manuela Luminita Bujorianu},
title = {Constructive Potential Theory: A Linear Logic Approach },
month = {June},
year = {2002},
pages = {182-196},
keywords = {determinacy analysis, Craig interpolants},
note = {Mini-symposion {"}Reuniting the Antipodes II: Constructive and Nonstandard Views of the Continuum{"}},
doi = {},
url = {http://www.cs.kent.ac.uk/pubs/2002/1525},
editor = {A. Berarducci and N.J. Cutland},
publication_type = {inproceedings},
submission_id = {22625_1033995796},
booktitle = {NS 2002 Non-standard Methods and Applications in Mathematics},
address = {Pisa, Italy},
organization = {AMS-UMI},
publisher = {University of Pisa},
refereed = {Yes},
}