Transience of continuous-time conservative random walks

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