We prove the existence and uniqueness of the L$$-variational solution, with p > 1, of the following multivalued backward stochastic differential equation with p-integrable data:
| $$ |
where τ is a stopping time, Q is a progressively measurable increasing continuous stochastic process and ∂$$Ψ is the subdifferential of the convex lower semicontinuous function y↦Ψ(t, y). In the framework of [14] (the case p ≥ 2), the strong solution found it there is the unique variational solution, via the uniqueness property proved in the present article.
Keywords: Backward stochastic differential equations, subdifferential operators, Stochastic variational inequalities, $$-integrable data
@article{COCV_2021__27_1_A90_0,
author = {Maticiuc, Lucian and R\u{a}\c{s}canu, Aurel},
title = {\protect\emph{ $L^p${}-Variational} solutions of multivalued backward stochastic differential equations},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2021},
publisher = {EDP-Sciences},
volume = {27},
doi = {10.1051/cocv/2021083},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2021083/}
}
TY - JOUR AU - Maticiuc, Lucian AU - Răşcanu, Aurel TI - $L^p$-Variational solutions of multivalued backward stochastic differential equations JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2021 VL - 27 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2021083/ DO - 10.1051/cocv/2021083 LA - en ID - COCV_2021__27_1_A90_0 ER -
%0 Journal Article %A Maticiuc, Lucian %A Răşcanu, Aurel %T $L^p$-Variational solutions of multivalued backward stochastic differential equations %J ESAIM: Control, Optimisation and Calculus of Variations %D 2021 %V 27 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv/2021083/ %R 10.1051/cocv/2021083 %G en %F COCV_2021__27_1_A90_0
Maticiuc, Lucian; Răşcanu, Aurel. $L^p$-Variational solutions of multivalued backward stochastic differential equations. ESAIM: Control, Optimisation and Calculus of Variations, Tome 27 (2021), article no. 88. doi: 10.1051/cocv/2021083
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