René L. Schilling

Bernstein Functions: Theory and Applications

This text is a self-contained and unified approach to Bernstein functions and their subclasses, bringing together old and establishing new connections. Applications of Bernstein functions in different fields of mathematics are given, with special attention to interpretations in probability theory. An extensive list of complete Bernstein functions with their representations is provided. A self-contained and unified approach to the topic With applications to various fields of mathematics, such as probability theory, potential theory, operator theory, integral equations, functional calculi and complex analysis With an extensive list of complete Bernstein functions.

Measures, integrals and martingales

p 20, Problem 3.5 be subsets of X be nonempty subsets of X p 20, Problem 3.5 (i) no proper subset B ( A no proper subset ∅ 6= B ( A p 20, Problem 3.9 Is this still true for the family B′ := {Br(x) : x ∈ Qn, r ∈ Q+} ? Denote by Br(x) an open ball in Rn with centre x and radius r. Show that the Borel sets B(Rn) are generated by the family of open balls B := {Br(x) : x ∈ Rn, r > 0}. Is this still true for the family B′ := {Br(x) : x ∈ Qn, r ∈ Q+} ? p 26, line 6 below from Example 2.3(v) from Example 3.3(v) p 31, line 10 below D,E ∈ E, D ∩ E = ∅ D,E ∈ D, D ∩ E = ∅ p 35, line 10 above invoke T5.5 invoke T5.7 p 36, Problem 5.3 for all A,B ∈ D for all A,B ∈ D with A ⊂ B p 36, Problem 5.8 Mimic the proof of Theorem 5.8(I). . . Mimic the proof of Theorem 5.8(i). . .

Conservativeness and Extensions of Feller Semigroups

AbstractLet

A note on the existence of transition probability densities of Lévy processes

\{ T_t \} _{t \geqslant 0}

Lévy-Type Processes and Pseudodifferential Operators

denote a Feller semigroup on

Some theorems on Feller processes: transience, local times and ultracontractivity

C_\infty (\mathbb{R}^n )