On existence and uniqueness of solutions to uncertain backward stochastic differential equations
- 159 Downloads
This paper is concerned with a class of uncertain backward stochastic differential equations (UBSDEs) driven by both an m-dimensional Brownian motion and a d-dimensional canonical process with uniform Lipschitzian coefficients. Such equations can be useful in modelling hybrid systems, where the phenomena are simultaneously subjected to two kinds of uncertainties: randomness and uncertainty. The solutions of UBSDEs are the uncertain stochastic processes. Thus, the existence and uniqueness of solutions to UBSDEs with Lipschitzian coefficients are proved.
KeywordsUncertain backward stochastic differential equations (UBSDEs) canonical process existence and uniqueness Lipschitzian condition martingale representation theorem
MR Subject Classification60H10 94D05
Unable to display preview. Download preview PDF.
- W Y Fei, Y H Li, C Fei. Properties of solutions to stochastic set differential equations under non-Lipschitzian coefficients, Abstr Appl Anal, http://www.hindawi.com/journals/aaa/aip/381972/.
- B Liu. Uncertainty Theory, 4th Ed, http://www.orsc.edu.cn/liu/.
- H J Liu, W Y Fei. Neutral uncertain delay differential equations, Information, 2013, 16(2): 1225–1232.Google Scholar
- H J Liu, H Ke, W Y Fei. Almost sure stability for uncertain differential equations, Fuzzy Optim Decis Mak, to be published.Google Scholar