Spectral analysis of subordinate Brownian motions on the half-line

• Autorzy: Mateusz Kwaśnicki
• Języki publikacji: EN

Abstrakty

EN

We study one-dimensional Lévy processes with Lévy-Khintchine exponent ψ(ξ²), where ψ is a complete Bernstein function. These processes are subordinate Brownian motions corresponding to subordinators whose Lévy measure has completely monotone density; or, equivalently, symmetric Lévy processes whose Lévy measure has completely monotone density on (0,∞). Examples include symmetric stable processes and relativistic processes. The main result is a formula for the generalized eigenfunctions of transition operators of the process killed after exiting the half-line. A generalized eigenfunction expansion of the transition operators is derived. As an application, a formula for the distribution of the first passage time (or the supremum functional) is obtained.

Kategorie tematyczne

• 60J35: Transition functions, generators and resolvents
• 60G52: Stable processes
• 60G51: Processes with independent increments; L\'evy processes
• 47G30: Pseudodifferential operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2011
• Tom: 206
• Numer: 3
• Strony: 211-271

Daty

wydano

2011

Twórcy

autor

Mateusz Kwaśnicki

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-976 Warszawa, Poland
• Institute of Mathematics and Computer Science, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

Identyfikatory

DOI

10.4064/sm206-3-2