期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2014
卷号：XI
页码：299-306
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：The main aim of this note is to nd an explicit integral formula forthe heat kernel of a certain second-order left invariant di erential operator on asolvable Lie group, being a semi-direct product RnR; by means of a skew-productformula for di usions. An explicit formula of a di erent kind for the special caseof the operator considered in this note (the operator without the drift term) wasfound recently by Calin, Chang and Li.As a corollary from our main result we get a simple formula for the returnprobability from which the asymptotic behaviour for small and large values of timefollows easily.
关键词：Heat kernel; elliptic operators; left invariant di erential operators;evolution equation; Brownian motion; di usion process; exponential functionals of Brownian mo-;tion; skew-product formula; return probability.
