Abstract
We give a Gaussian-type upper bound for the transition kernels of the time-inhomogeneous diffusion processes on a nilpotent meta-abelian Lie group N generated by the family of time dependent second order left-invariant differential operators. These evolution kernels are related to the heat kernel for the left-invariant second order differential operators on higher rank NA groups.
Highlights
Time-dependent parabolic equations and, in particular, the problem of finding the upper and lower bounds for their fundamental solutions has attracted considerable attention in recent years
Urban type upper bound for the transition kernel of a particular kind of diffusion process on a nilpotent meta-abelian group N
In what follows we assume that the group N is meta-abelian
Summary
Time-dependent parabolic equations and, in particular, the problem of finding the upper and lower bounds for their fundamental solutions has attracted considerable attention in recent years (see e.g. [5,12,13,14,15,31] and the monographs by Stroock and Varadhan [27], and van Casteren [4]). Time-dependent parabolic equations and, in particular, the problem of finding the upper and lower bounds for their fundamental solutions has attracted considerable attention in recent years [5,12,13,14,15,31] and the monographs by Stroock and Varadhan [27], and van Casteren [4]). Urban type upper bound for the transition kernel of a particular kind of diffusion process (evolution) on a nilpotent meta-abelian group N. The type of the evolution equation considered here comes from the study of the heat equation on a class of solvable Lie groups, the so called higher rank N A groups which are, by definition, the semi-direct products of a nilpotent and abelian (with dimension greater than 1) groups
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