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-α , 0<α≤ 1 , or the law (\!ln t)-β where β>2 .