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

Citation:

Guang YANG.Multi-dimensional Backward Stochastic Differential Equations of DiagonallyQuadratic Generators with a Special Structure[J].Chinese Annals of Mathematics B,2024,45(6):855~868
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Authors:

Guang YANG;

Foundation:

the National Natural Science Foundation of China (Nos. 11631004, 12031009).
Abstract: 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 6= i). Finally, a solvability result is given when the diagonally quadratic generator is triangular.

Keywords:

Multi-dimensional BSDE, Diagonally quadratic generator, BMO martingale

Classification:

60H10
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