We study a class of degenerate elliptic second order differential operators acting on some polynomial weighted function spaces on [0, +∞[. We show that these operators are the generators of C_0-semigroups of positive operators which, in turn, are the transition semigroups associated with right-continuous normal Markov processes with state space [0, +∞]. 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.

On a class of elliptic-parabolic equations on unbounded intervals

MANGINO, Elisabetta Maria
2001-01-01

Abstract

We study a class of degenerate elliptic second order differential operators acting on some polynomial weighted function spaces on [0, +∞[. We show that these operators are the generators of C_0-semigroups of positive operators which, in turn, are the transition semigroups associated with right-continuous normal Markov processes with state space [0, +∞]. 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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11587/102039
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