| Issue |
ESAIM: M2AN
Volume 59, Number 3, May-June 2025
|
|
|---|---|---|
| Page(s) | 1333 - 1363 | |
| DOI | https://doi.org/10.1051/m2an/2024086 | |
| Published online | 27 May 2025 | |
Convergence of particles and tree based scheme for singular FBSDEs
1
ENSAE-CREST and Institut Polytechnique de Paris, Palaiseau, France
2
UFR de Mathématiques & LPSM, Université Paris Cité, Bâtiment Sophie Germain, 8 place Aurélie Nemours, 75013 Paris, France
* Corresponding author: chassagneux@ensae.fr
Received:
6
March
2023
Accepted:
30
December
2024
We study an implementation of the theoretical splitting scheme introduced in Chassagneux and Yang (J. Comput. Phys. 468 (2022) 111459) for singular FBSDEs (Carmona and Delarue, Probab. Theory Relat. Fields 157 (2013) 333–388) and their associated quasi-linear degenerate PDEs. The fully implementable algorithm is based on particles approximation of the transport operator and tree like approximation of the diffusion operator appearing in the theoretical splitting. We prove the convergence with a rate of our numerical method under some reasonable conditions on the coefficients functions. This validates a posteriori some numerical results obtained in Chassagneux and Yang (J. Comput. Phys. 468 (2022) 111459). We conclude the paper with a numerical section presenting various implementations of the algorithm and discussing their efficiency in practice.
Mathematics Subject Classification: 65C30 / 65C20 / 65M12 / 60H35
Key words: Singular FBSDEs / probabilistic methods / splitting scheme / particle method
© The authors. Published by EDP Sciences, SMAI 2025
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