Asymptotic stability of neutral-type stochastic functional differential equations; Collaborative research visit to China

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The proposed collaboration is mainly to study the asymptotic stability of neutral-type stochastic functional differential equations. Shen and the PI already have an ongoing collaboration in this area. The collaboration was initiated in 2004 when the PI visited China. The collaboration has since continued mainly via e-mails. Three papers resulting from the collaboration to date have been published or accepted for publication. In these papers, we have not only established some very interesting results on stochastic stability but also identified some new problems. For example, it is observed that the existing stability criteria on neutral-type equations require the linear growth condition and constant delay. Moreover, there is little known about the stability of numerical methods applied to neutral-type equations. To get insight on these problems, we write this proposal for a travel grant for the PI to visit Shen's laboratory in order to continueour current collaboration, namely to carry out a project with 3 aims listed above. The key benefits are:(1) to give the PI an opportunity to have face-to-face discussions with Professor Shen as well as other researchers visiting Professor Shen's Laboratory;(2) to make use of the excellent computing facility in Professor Shen's laboratory to carry out the computational side of the project.