Exponential stability of stochastic delay differential equation driven by Lévy noise (Q2910585)

The author extends \textit{X. Mao} and \textit{A. Shah}'s [Stochastics Stochastics Rep. 60, No. 1--2, 135--153 (1997; Zbl 0872.60045)] and \textit{D. Applebaum} and \textit{M. Siakalli}'s [J. Appl. Probab. 46, No. 4, 1116--1129 (2009; Zbl 1185.60058)] technique to the case of nonlinear stochastic differential equation driven by Levy noise of the form NEWLINE\[NEWLINEdx(t)=f(x(t-\tau))dt+g(x(t-\tau))dw(t)+\int_{|y|>c} H(x(t),y)\tilde{N}(dt, dy),\; \; t\geq 0.NEWLINE\]NEWLINE The main result is given in Theorem 2.3. The prof uses a lemma from [X. Mao and A. Shah, loc. cit.]. This result extends the linear case, see [\textit{C. W. Li, Z. Dong} and \textit{R. Situ}, Probab. Theory Relat. Fields 123, No. 1, 121--155 (2002; Zbl 1019.34055)] and a nonlinear result with compound Poisson noise (see M. Grigoriu, 1992).