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Feynman-Kac penalisations of symmetric stable processes. (English) Zbl 1193.60096
Summary: In K. Yano, Y. Yano and M. Yor [J. Math. Soc. Japan 61, No. 3, 757–798 (2009 (2009; Zbl 1180.60008)], limit theorems for the one-dimensional symmetric $$\alpha$$-stable process normalized by negative (killing) Feynman-Kac functionals were studied. We consider the same problem and extend their results to positive Feynman-Kac functionals of multi-dimensional symmetric $$\alpha$$-stable processes.

##### MSC:
 60J45 Probabilistic potential theory 60J40 Right processes 35J10 Schrödinger operator, Schrödinger equation
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