✦ LIBER ✦

Degenerate elliptic operators, Feller semigroups and modified Bernstein-Schnabl operators

✍ Scribed by Francesco Altomare; Mirella Cappelletti Montano; Sabrina Diomede

Publisher: John Wiley and Sons
Year: 2011
Tongue: English
Weight: 200 KB
Volume: 284
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200810196

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

In this paper we study a class of elliptic second‐order differential operators on finite dimensional convex compact sets whose principal part degenerates on a subset of the boundary of the domain. We show that the closures of these operators generate Feller semigroups.

Moreover, we approximate these semigroups by iterates of suitable positive linear operators which we also introduce and study in this paper for the first time, and which we refer to as modified Bernstein‐Schnabl operators. As a consequence of this approximation we investigate some regularity properties preserved by the semigroup.

Finally, we consider the special case of the finite dimensional simplex and the well‐known Wright‐Fisher diffusion model of gene frequency used in population genetics. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim

📜 SIMILAR VOLUMES

Analytic Semigroups and Degenerate Ellip

Analytic Semigroups and Degenerate Elliptic Operators with Unbounded Coefficients: A Probabilistic Approach

✍ Sandra Cerrai 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 176 KB

By using techniques derived from the theory of stochastic differential equations, we prove that a class of second order degenerate elliptic operators having unbounded coefficients generates analytic semigroups in C b (R d ), the space of uniformly continuous and bounded functions from R d into R.