Issue |
ESAIM: COCV
Volume 27, 2021
|
|
---|---|---|
Article Number | 88 | |
Number of page(s) | 73 | |
DOI | https://doi.org/10.1051/cocv/2021083 | |
Published online | 09 August 2021 |
Lp-Variational solutions of multivalued backward stochastic differential equations
1
Faculty of Mathematics, “Alexandru Ioan Cuza” University, Carol I Blvd., no. 11,
700506
Iaşi, Romania.
2
“Octav Mayer” Institute of Mathematics of the Romanian Academy, Carol I Blvd., no. 8,
700506
Iaşi, Romania.
* Corresponding author: lucian.maticiuc@uaic.ro
Received:
25
February
2020
Accepted:
6
July
2021
We prove the existence and uniqueness of the Lp-variational solution, with p > 1, of the following multivalued backward stochastic differential equation with p-integrable data: {−dYt + ∂yΨ(t,Yt)dQt∋H(t,Yt,Zt)dQt−ZtdBt,0≤t<τ, Yτ = η,
where τ is a stopping time, Q is a progressively measurable increasing continuous stochastic process and ∂yΨ is the subdifferential of the convex lower semicontinuous function y↦Ψ(t, y). In the framework of [14] (the case p ≥ 2), the strong solution found it there is the unique variational solution, via the uniqueness property proved in the present article.
Mathematics Subject Classification: 60H10 / 60F25 / 47J20 / 49J40
Key words: Backward stochastic differential equations / subdifferential operators / Stochastic variational inequalities / p-integrable data
© The authors. Published by EDP Sciences, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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