Backward Stochastic Differential Equations with No Driving Martingale, Markov Processes and Associated Pseudo-Partial Differential Equations: Part II—Decoupled Mild Solutions and Examples

Adrien Barrasso () and Francesco Russo ()
Additional contact information
Adrien Barrasso: Université d’Évry Val d’Essonne
Francesco Russo: Unité de Mathématiques appliquées

Journal of Theoretical Probability, 2021, vol. 34, issue 3, 1110-1148

Abstract: Abstract Let $$(\mathbb {P}^{s,x})_{(s,x)\in [0,T]\times E}$$ ( P s , x ) ( s , x ) ∈ [ 0 , T ] × E be a family of probability measures, where E is a Polish space, defined on the canonical probability space $${\mathbb D}([0,T],E)$$ D ( [ 0 , T ] , E ) of E-valued càdlàg functions. We suppose that a martingale problem with respect to a time-inhomogeneous generator a is well-posed. We consider also an associated semilinear Pseudo-PDE for which we introduce a notion of so-called decoupled mild solution and study the equivalence with the notion of martingale solution introduced in a companion paper. We also investigate well-posedness for decoupled mild solutions and their relations with a special class of backward stochastic differential equations (BSDEs) without driving martingale. The notion of decoupled mild solution is a good candidate to replace the notion of viscosity solution which is not always suitable when the map a is not a PDE operator.

Keywords: Martingale problem; Pseudo-PDE; Markov process; Backward stochastic differential equation; Decoupled mild solution; 60H30; 60H10; 35S05; 60J35; 60J60; 60J99 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10959-021-01092-7 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:jotpro:v:34:y:2021:i:3:d:10.1007_s10959-021-01092-7

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-021-01092-7

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().