Introduction and Main Results

Kazuaki Taira ()
Additional contact information
Kazuaki Taira: University of Tsukuba, The College of Mathematics

Chapter Chapter 1 in Real Analysis Methods for Markov Processes, 2024, pp 1-18 from Springer

Abstract: Abstract This book provides a careful and accessible exposition of the functional analytic approach to the problem of construction of strong Markov processes with Ventcel’ (Wentzell) boundary conditions in probability theory (see the last Chap. 26 ). More precisely, we prove existence theorems for $$T_{t}$$ T t (Feller semigroup) Feller semigroups with Dirichlet boundary condition, oblique derivative boundary condition and first order Ventcel’ boundary condition for second order, uniformly elliptic differential operators with discontinuous coefficients. Our approach here is distinguished by the extensive use of the ideas and techniques characteristic of the recent developments in the Calderón–Zygmund theory of singular integral operators with non-smooth kernels (see [33–35, 140, 166, 167]). It should be emphasized that there is an approximate functional calculus for such operators resembling the Fourier transform apparatus (see [22–26, 28, 137]).

Date: 2024
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-97-3659-1_1

Ordering information: This item can be ordered from
http://www.springer.com/9789819736591

DOI: 10.1007/978-981-97-3659-1_1

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().