Local wellposedness of coupled backward stochastic differential equations driven by G-Brownian motions

Zheng, Guoqiang

doi:10.1016/j.jmaa.2021.125540

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Doob-meyer Decomposition Theorem1

Introduction1

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2022

2023

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“…Proof. Consider the following conformable backward stochastic differential equation: (13) where ζ ∈ L 2 (Ω, F T , P), a ≤ t ≤ T, 0 < ρ ≤ 1 and n = 1, 2, 3, • • •.…”

Section: Doob-meyer Decomposition Theoremmentioning

confidence: 99%

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g-Expectation for Conformable Backward Stochastic Differential Equations

Luo

Fečkan

Wang

et al. 2022

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In this paper, we study the applications of conformable backward stochastic differential equations driven by Brownian motion and compensated random measure in nonlinear expectation. From the comparison theorem, we introduce the concept of g-expectation and give related properties of g-expectation. In addition, we find that the properties of conformable backward stochastic differential equations can be deduced from the properties of the generator g. Finally, we extend the nonlinear Doob–Meyer decomposition theorem to more general cases.

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“…Proof. Consider the following conformable backward stochastic differential equation: (13) where ζ ∈ L 2 (Ω, F T , P), a ≤ t ≤ T, 0 < ρ ≤ 1 and n = 1, 2, 3, • • •.…”

Section: Doob-meyer Decomposition Theoremmentioning

confidence: 99%

“…In addition, coupled forward backward stochastic differential equations driven by the G-Brownian motion were studied in [13], while [14] investigated the solvability of fully coupled forward-backward stochastic differential equations with irregular coefficients.…”

Section: Introductionmentioning

confidence: 99%