Picture of scraped petri dish

Scrape below the surface of Strathprints...

Explore world class Open Access research by researchers at the University of Strathclyde, a leading technological university.

Explore

Numerical solutions of stochastic differential delay equations under the generalized Khasminskii-type conditions

Mao, Xuerong (2011) Numerical solutions of stochastic differential delay equations under the generalized Khasminskii-type conditions. Applied Mathematics and Computation, 217 (12). pp. 5512-5524. ISSN 0096-3003

Full text not available in this repository. (Request a copy from the Strathclyde author)

Abstract

The classical existence-and-uniqueness theorem of the solution to a stochastic differential delay equation (SDDE) requires the local Lipschitz condition and the linear growth condition (see e.g. [11], [12] and [20]). The numerical solutions under these conditions have also been discussed intensively (see e.g. [4], [10], [13], [16], [17], [18], [21], [22] and [24]). Recently, Mao and Rassias [14] and [15] established the generalized Khasminskii-type existence-and-uniqueness theorems for SDDEs, where the linear growth condition is no longer imposed. These generalized Khasminskii-type theorems cover a wide class of highly nonlinear SDDEs but these nonlinear SDDEs do not have explicit solutions, whence numerical solutions are required in practice. However, there is so far little numerical theory on SDDEs under these generalized Khasminskii-type conditions. The key aim of this paper is to close this gap.