Markovian integral equations

Kalinin, Alexander (2020): Markovian integral equations. In: Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, Bd. 56, Nr. 1: S. 155-174

Abstract

We analyze multidimensional Markovian integral equations that are formulated with a progressive time-inhomogeneous Markov process that has Borel measurable transition probabilities. In the case of a path process of a path-dependent diffusion, the solutions to these integral equations lead to the concept of mild solutions to path-dependent partial differential equations (PPDEs). Our goal is to establish uniqueness, stability, existence and non-extendibility of solutions among a certain class of maps. By requiring the Feller continuity of the Markov process, we give weak conditions under which solutions become continuous. Moreover, we provide a multidimensional Feynman–Kac formula and a one-dimensional global existence and uniqueness result.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik > Finanz- und Versicherungsmathematik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 0246-0203
• Sprache: Englisch