Almost sure exponential stability of the backward Euler–Maruyama scheme for stochastic delay differential equations with monotone-type condition

Lin Chen ^[1] ; Fuke Wu ^[2]
1. [1] Jiangxi University of Finance and Economics
  
  Jiangxi University of Finance and Economics
  
  China
2. [2] Huazhong University of Science and Technology
  
  Huazhong University of Science and Technology
  
  China
Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 282, Nº 1 (July 2015), 2015, págs. 44-53
Idioma: inglés
DOI: 10.1016/j.cam.2014.12.036
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Resumen
- This paper is a continuation of our previous paper, in which, the second author, with Mao and Szpruch examined the almost sure stability of the Euler–Maruyama (EM) and the backward Euler–Maruyama (BEM) methods for stochastic delay differential equations (SDDEs). In the previous results, although the drift coefficient may defy the linear growth condition, the diffusion coefficient is required to satisfy the linear growth condition. In this paper we want to further relax the condition. Under monotone-type condition, this paper will give the almost sure stability of the BEM for SDDEs whose both drift and diffusion coefficients may defy the linear condition. This improves the existing results considerably.