Khasminskii-type theorems for stochastic functional differential equations

Minghui Song, Liangjian Hu, Xuerong Mao, Liguo Zhang

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)


For a stochastic functional differential equation (SFDE) to have a unique global solution it is in general required that the coefficients of the SFDE obey the local Lipschitz condition and the linear growth condition. However, there are many SFDEs in practice which do not obey the linear growth condition. The main aim of this paper is to establish existence-and-uniqueness theorems for SFDEs where the linear growth condition is replaced by more general Khasminskii-type conditions in terms of a pair of Laypunov-type functions.
Original languageEnglish
Pages (from-to)1697-1714
Number of pages18
JournalDiscrete and Continuous Dynamical Systems - Series B
Issue number6
Publication statusPublished - Aug 2013


  • Brownian motion
  • Ito's formula
  • Khasminskii-test


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