Shiga–Watanabe's time inversion property for self-similar diffusion processes

Abstract

Assume ( X t , P 0 ) is 1 2 -self-similar, rotation invariant diffusion on R d , d ⩾ 2 , starting at 0 and assume {0} is a polar set. We will show, using the corresponding well-known result for the radial process, that Shiga–Watanabe's time inversion property holds for ( X t , P 0 ) . The generalization for an α -self-similar, rotation invariant diffusion, α > 0 , is also given.