Lévy型算子所生成马氏过程的稳定性

Stability of Markov Processes Generated by Lévy Type Operators

利用Levy型算子积分微分型表示形式和拟微分型表示形式,以寻求Levy型算子生成的马氏过程各种稳定性的精确且可验证的充分条件.给出了由符号函数直接判定的Levy型过程非爆炸的充分条件,这个条件包括了扩散过程非爆炸的线性增长条件;当Levy型算子生成马氏过程对应半群的符号函数已知时,得到了由该符号函数直接表达的常返性充分条件,它推广了关于Levy过程经典的Chung-Fuchs常返性准则.

Based on both integral-differential representation and pseudo-differential representation of Levy type operator,explicit and verifiable conditions about non-explosion and other stabilities of Markov processes generated by Levy type operators are derived.A sufficient condition for non-explosion in term of the symbol is given,which includes linear growth conditions for conservative diffusions;when the symbol of the corresponding semigroups generated by Levy type operator is known explicitly,the author obtains a direct recurrent condition involving this symbol,which extends the classic Chung-Fuchs＇s criterion for Levy processes.