ON LEFT INVARIANT BROWNIAN MOTIONS AND HEAT KERNELS OF NILPOTENT LIE-GROUPS

Left-invariant Brownian motions on nilpotent Lie groups are studied. Their characterization is given through Ito or Stratonovich stochastic differential equations, their generators are exhibited and the associated heat semigroups are studied. A reduction formula is given for these semigroups and their kernels, as integrals of products of normalized random Gaussian densities. © 1990 American Institute of Physics.