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For:
Wu Z
, Xu M.
Comparison theorems for forward backward SDEs.
Stat Probab Lett
2009. [DOI:
10.1016/j.spl.2008.09.011
]
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Citation(s) in
RCA
: 9
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[
Impact Index Per Article: 0.6
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[Indexed: 11/28/2022]
Number
Cited by Other Article(s)
1
Backward Doubly Stochastic Differential Equations with Markov Chains and a Comparison Theorem.
Symmetry (Basel)
2020. [DOI:
10.3390/sym12121953
]
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Citation(s) in
RCA
: 2
]
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Impact Index Per Article: 0.5
]
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[Indexed: 11/16/2022]
Open
Abstract
In this paper we study the existence and uniqueness of solutions for one kind of backward doubly stochastic differential equations (BDSDEs) with Markov chains. By generalizing the Itô’s formula, we study such problem under the Lipschitz condition. Moreover, thanks to the Yosida approximation, we solve such problem under monotone condition. Finally, we give the comparison theorems for such equations under the above two conditions respectively.
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2
Ma J
, Wu Z, Zhang D, Zhang J. On well-posedness of forward–backward SDEs—A unified approach.
ANN APPL PROBAB
2015. [DOI:
10.1214/14-aap1046
]
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Citation(s) in
RCA
: 67
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Impact Index Per Article: 7.4
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[Indexed: 11/19/2022]
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3
Ma J
, Yin H, Zhang J. On non-Markovian forward–backward SDEs and backward stochastic PDEs.
Stoch Process Their Appl
2012. [DOI:
10.1016/j.spa.2012.08.002
]
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Citation(s) in
RCA
: 17
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Impact Index Per Article: 1.4
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[Indexed: 10/28/2022]
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