Transience of continuous-time conservative random walks

Abstract

We consider two continuous-time generalizations of conservative random walks introduced in [J.Englander and S.Volkov (2022)], an orthogonal and a spherically-symmetrical one; the latter model is known as {\em random flights}. For both models, we show the transience of the walks when $d\ge 2$ and the rate of changing of direction follows power law $t^{-\hat{I}\pm }$, $0<\hat{I}\pm \le 1$, or the law $(\ln t{)}^{-{\hat{I}}^2}$ where ${\hat{I}}^2>2$.