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 >= 2 and that the rate of direction changing follows a power law t(-alpha),0 < alpha <= 1, or the law (lnt)(-beta) where beta > 2.