马氏过程的随机稳定性是随机分析理论的重要研究分支。一般来说，随机稳定性包括常返性和非常返性两大类，关于常返性的研究结果已经相当丰富，而对非常返性的研究却相对较少。本项目主要讨论连续时间马氏过程的一种最常见的非常返性—指数非常返性。首先，我们拟研究指数非常返性的判别准则，计划得到关于广义生成元的Foster-Lyapunov条件和某集合击中时的矩条件。其次，我们考虑利用Foster-Lyapunov条件，并将Lévy型算子与扩散算子作比较，研究由Lévy过程驱动的随机微分方程指数非常返性的显示判别。最后，本项目计划利用Foster-Lyapunov条件和对偶变换估计L^2指数衰减速度，进而研究指数非常返的收敛速度。

Stochastic stability for Markov process is an important branch of stochastic analysis. It is well known that recurrence and transience are two important stochastic stabilities. Comparing with the abundant study concerning recurrence, however, known results on transience are quite limited. The project is mainly devoted to discussing the exponential transience for continuous-time Markov processes. First, criteria for exponential transience will be presented through establishing the appropriate Foster-Lyapunov condition for the extended generator, or bounding the moment of the hitting time to some set. Moreover, by using the Foster-Lyapunov condition and comparing Lévy type operators with diffusion operators, we aim to study the exponential transience for stochastic differential equations driven by Lévy processes. Finally, we shall estimate the L^2-exponential decay by the Foster-Lyapunov condition and duality, and then investigate the convergence rates of exponential transience.