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Multi-dimensional Backward Stochastic Differential Equations of Diagonally Quadratic Generators with a Special Structure

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Multi-dimensional Backward Stochastic Differential Equations of Diagonally Quadratic Generators with a Special Structure
The present paper is devoted to the well-posedness of a type of multi-dimensional backward stochastic differential equations(BSDE for short)with a diagonally quadratic generator.The author gives a new priori estimate,and prove that the BSDE admits a unique solution on a given interval when the generator has a sufficiently small growth of the off-diagonal elements(i.e.,for each i,the i-th component of the generator has a small growth of the j-th row zj of the variable z for each j≠i).Finally,a solvability result is given when the diagonally quadratic generator is triangular.

Multi-dimensional BSDEDiagonally quadratic generatorBMO martingale

Guang YANG

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Shanghai Center for Mathematical Sciences,Fudan University,Shanghai 200433,China

Multi-dimensional BSDE Diagonally quadratic generator BMO martingale

2024

数学年刊B辑(英文版)
国家教育部委托复旦大学主办

数学年刊B辑(英文版)

CSTPCD
影响因子:0.129
ISSN:0252-9599
年,卷(期):2024.45(6)