Constructive Potential Theory: A Linear Logic Approach

Bujorianu, Marius C. and Bujorianu, Manuela L. (2002) Constructive Potential Theory: A Linear Logic Approach. In: NS 2002 Non-standard Methods and Applications in Mathematics, June 2002, Pisa, Italy. (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

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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.

Item Type: Conference or workshop item (UNSPECIFIED)
Additional information: Mini-symposion ''Reuniting the Antipodes II: Constructive and Nonstandard Views of the Continuum''
Uncontrolled keywords: Potential theory, constructive analysis, linear logic
Subjects: Q Science > QA Mathematics (inc Computing science) > QA 76 Software, computer programming,
Divisions: Faculties > Science Technology and Medical Studies > School of Computing > Theoretical Computing Group
Depositing User: Mark Wheadon
Date Deposited: 24 Nov 2008 18:00
Last Modified: 09 May 2012 09:57
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