Journal
APPLIED MATHEMATICS AND COMPUTATION
Volume 220, Issue -, Pages 53-62Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2013.05.054
Keywords
Anticipated backward doubly stochastic differential equation; Comparison theorem; Duality
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Funding
- Mathematical Tianyuan Foundation of China [11126050]
- Specialized Research Fund for the Doctoral Program of Higher Education of China [20113207120002]
- National Natural Science Foundation of China [11101209]
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In this paper, we deal with a new type of differential equations called anticipated backward doubly stochastic differential equations (anticipated BDSDEs). The coefficients of these BDSDEs depend on the future value of the solution (Y,Z). We obtain the existence and uniqueness theorem and a comparison theorem for the solutions of these equations. Besides, as an application, we also establish a duality between the anticipated BDSDEs and the delayed doubly stochastic differential equations (delayed DSDEs). (C) 2013 Elsevier Inc. All rights reserved.
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