Open Access Open Access  Restricted Access Subscription or Fee Access

Almost Sure Asymptotic Estimations for Solutions of Stochastic Differential Delay Equations

Xuerong Mao, Matina John Rassias

Abstract


The classical Khasminskii theorem (see [7]) on the non-explosion solutions of stochastic differential equations (SDEs) is very important since it gives a powerful test for SDEs to have non-explosion solutions without the linear growth condition. Recently, we [15] established a more general Khasminskii-type test for stochastic differential delay equations (SDDEs) which covers a wide class of highly non-linear SDDEs. We also give some interesting and useful moment estimations. This paper is a continuation of our earlier one and the main aim is to establish almost sure asymptotic estimations.

Keywords


Brownian motion, stochastic differential delay equation, Ito’s formula, Gronwall inequality, asymptotic estimation.

Full Text:

PDF


Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information. Also: DOI is paid service which provided by a third party. We never mentioned that we go for this for our any journal. However, journal have no objection if author go directly for this paid DOI service.