# American Institute of Mathematical Sciences

September  2018, 17(5): 2125-2133. doi: 10.3934/cpaa.2018100

## Order preservation for path-distribution dependent SDEs

 1 Center for Applied Mathematics, Tianjin University, Tianjin 300072, China 2 School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China 3 Department of Mathematics, Swansea University, Singleton Park, SA2 8PP, United Kingdom

* Corresponding author

Received  October 2017 Revised  January 2018 Published  April 2018

Fund Project: The third author is supported by NNSFC (11771326, 11431014).

Sufficient and necessary conditions are presented for the order preservation of path-distribution dependent SDEs. Differently from the corresponding study of distribution independent SDEs, to investigate the necessity of order preservation for the present model we need to construct a family of probability spaces in terms of the ordered pair of initial distributions.

Citation: Xing Huang, Chang Liu, Feng-Yu Wang. Order preservation for path-distribution dependent SDEs. Communications on Pure & Applied Analysis, 2018, 17 (5) : 2125-2133. doi: 10.3934/cpaa.2018100
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