Publication Date:
2014-08-14
Description:
In the paper, our main aim is to investigate the strong convergence and almost surely exponential stability of an implicit numerical approximation under one-sided Lipschitz condition and polynomial growth condition on the drift coefficient, and polynomial growth condition on the diffusion coefficient. After providing almost surely exponential stability and moment boundedness for the exact solution, we show that an appropriate implicit numerical method preserves boundedness of moments, and the numerical approximation converges strongly to the true solution. Moreover, we prove that the backward Euler–Maruyama approximation can share almost surely exponential stability of the exact solution for sufficiently small step size.
Print ISSN:
0008-0624
Electronic ISSN:
1126-5434
Topics:
Mathematics
