L p Solutions for Multidimensional BDSDEs with Locally Weak Monotonicity Coefficients

Dejian Tian , Runyu Zhu

Chinese Annals of Mathematics, Series B ›› 2021, Vol. 42 ›› Issue (3) : 409 -426.

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Chinese Annals of Mathematics, Series B ›› 2021, Vol. 42 ›› Issue (3) : 409 -426. DOI: 10.1007/s11401-021-0266-5
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L p Solutions for Multidimensional BDSDEs with Locally Weak Monotonicity Coefficients

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Abstract

In this paper, the authors establish the existence and uniqueness theorem of L p (1 < p ≤ 2) solutions for multidimensional backward doubly stochastic differential equations (BDSDEs for short) under the p-order globally (locally) weak monotonicity conditions. Comparison theorem of L p solutions for one-dimensional BDSDEs is also proved. These conclusions unify and generalize some known results.

Keywords

Backward doubly stochastic differential equation / Locally monotonicity condition / L p solution

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Dejian Tian, Runyu Zhu. L p Solutions for Multidimensional BDSDEs with Locally Weak Monotonicity Coefficients. Chinese Annals of Mathematics, Series B, 2021, 42(3): 409-426 DOI:10.1007/s11401-021-0266-5

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