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Entrance and exit at infinity for stable jump diffusions. (English) Zbl 07226359
Summary: In his seminal work from the 1950s, William Feller classified all one-dimensional diffusions on $$-\infty\leq a< b\leq\infty$$ in terms of their ability to access the boundary (Feller’s test for explosions) and to enter the interior from the boundary. Feller’s technique is restricted to diffusion processes as the corresponding differential generators allow explicit computations and the use of Hille-Yosida theory. In the present article, we study exit and entrance from infinity for the most natural generalization, that is, jump diffusions of the form $dZ_t=\sigma (Z_{t-})\,dX_t,$
##### MSC:
 60H20 Stochastic integral equations 60G52 Stable stochastic processes
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