Transience of continuous-time conservative random walks

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 $t^{-\alpha }$, $0<\alpha \le 1$, or the law $(\ln t{)}^{-\beta }$ where $\beta >2$.