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Weighted bounded mean oscillation applied to backward stochastic differential equations

Institution:	1. Department of Mathematical Sciences, Seoul National University, Building 27, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, Republic of Korea;1. Institute of Mathematics, Polish Academy of Sciences, Św. Tomasza 30/7, 31-027 Kraków, Poland;2. Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland;1. Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy;2. Università di Torino, Dipartimento di Matematica “G. Peano”, Via Carlo Alberto 10, 10123 Torino, Italy

Abstract:	We deduce conditional $L_{p}$ -estimates for the variation of a solution of a BSDE. Both quadratic and sub-quadratic types of BSDEs are considered, and using the theory of weighted bounded mean oscillation we deduce new tail estimates for the solution $(Y, Z)$ on subintervals of $0, T]$ . Some new results for the decoupling technique introduced in Geiss and Ylinen (2019) are obtained as well and some applications of the tail estimates are given.

Keywords:	BSDEs Weighted bounded mean oscillation John–Nirenberg theorem Tail estimates Decoupling
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