Volume 27, 2021
|Number of page(s)||73|
|Published online||09 August 2021|
Lp-Variational solutions of multivalued backward stochastic differential equations
Faculty of Mathematics, “Alexandru Ioan Cuza” University, Carol I Blvd., no. 11,
2 “Octav Mayer” Institute of Mathematics of the Romanian Academy, Carol I Blvd., no. 8, 700506 Iaşi, Romania.
* Corresponding author: firstname.lastname@example.org
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:
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  (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
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