On a class of elliptic-parabolic equations on unbounded intervals

We study a class of degenerate elliptic second order differential operators acting on some polynomial weighted function spaces on [0,+[infinity][. We show that these operators are the generators of C0-semigroups of positive operators which, in turn, are the transition semigroups associated with righ...

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Bibliographic Details
Published in:Positivity : an international journal devoted to the theory and applications of positivity in analysis 2001-09, Vol.5 (3), p.239-257
Main Authors: ALTOMARE, Francesco, MANGINO, Elisabetta M
Format: Article
Language:English
Subjects:
Approximations and expansions
Banach spaces
Calculus
Exact sciences and technology
Markov analysis
Markov processes
Mathematical analysis
Mathematical functions
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Operator theory
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Probability and statistics
Probability theory and stochastic processes
Random variables
Sciences and techniques of general use
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Summary:We study a class of degenerate elliptic second order differential operators acting on some polynomial weighted function spaces on [0,+[infinity][. We show that these operators are the generators of C0-semigroups of positive operators which, in turn, are the transition semigroups associated with right-continuous normal Markov processes with state space [0,+[infinity]]. Approximation and qualitative properties of both the semigroups and the Markov processes are investigated as well. Most of the results of the paper depend on a representation of the semigroups we give in terms of powers of particular positive operators of discrete type we introduced and studied in a previous paper. [PUBLICATION ABSTRACT]
ISSN:1385-1292
1572-9281
DOI:10.1023/A:1011450903149