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WROCŁAW UNIVERSITY
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TECHNOLOGY

Contents of PMS, Vol. 17, Fasc. 2,
pages 339 - 364
 

PROPERTIES OF GREEN FUNCTION OF SYMMETRIC STABLE PROCESSES

Tadeusz Kulczycki

Abstract: We study the Green function G (x,y) D of symmetric a -stable processes in Rd for an open set D(0 < a < 2,d > 3). Our main result gives the upper and the lower bound estimates of G (x,y) D for a bounded open set D with a C1,1 boundary. We also get a more direct formula for the Green function for a ball. As a simple conclusion we obtain “3G Theorem” and estimates of Ex(t ), D where t D is the exit time of D.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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