In this paper, by the Burkholder-Davis-Gundy inequality and It formula, the exponential estimate of the solution to stochastic functional differential equations with infinite delay is established in the phase space BC((-∞,0];Rd). Furthermore, the sample Lyapunov exponent of the solution is obtained, which is less than a positive constant 2√K + 65K. Moreover, a pth moment of the solution is studied.
Fengying Wei (College of Math. and Computer Sci., Fuzhou University, Fuzhou 350108) Ke Wang (Dept. of Math., Harbin Institute of Technology, Weihai 264209, Shandong)
通过改进FRT算法,得到随机最小序分割算法(random minimum order partition,RMOP)。在度量空间G中,对点列V进行随机排序(设序列为π),随机选取点u∈V后,获得下标J r(u)=inf{j∈N:d(πj,u)≤r,πj,u∈V},再以点πJr(u)为球心r为半径,对度量空间G进行递归分割,进而形成一棵分层良分割树(hierarchically well separated tree,HST);同时得到E(d T(u,v))≤O(log n)d(u,v)。在RMOP算法与FRT算法具有相同的π时,RMOP算法能保证点u落入特定分割子集B(πJr(u),r)的概率最大。
In this paper,a kind of stochastic differential equation is investigated and the almost sure exponential stability of the equation is obtained using Gronwall's inequality.Further,we also give other noise intensity function to keep the stability of the system.
Wei Liu (Dept.of Math.,Public Security Marine Police Academy,Ningbo 315000,Zhejiang) Fengying Wei (College of Math.and Computer Sci.,Fuzhou University,Fuzhou 350108)
