We consider the telegraph process with two velocities, a1>a2∈R, and two rates of reversal, λ1,λ2>0. We study some of its features with respect to the conditional probability measure where both the initial speed and the number of changes of direction are known. We exhibit a new proof by induction of the (conditional) probability law and a detailed study of the distribution of the motion at time t>0 conditioned on its position at a previous time 00, its maximum and its minimum up to that moment.
A note on the conditional probabilities of the telegraph process / Cinque, F.. - In: STATISTICS & PROBABILITY LETTERS. - ISSN 0167-7152. - 185:(2022), p. 109431. [10.1016/j.spl.2022.109431]
A note on the conditional probabilities of the telegraph process
Cinque F.
2022
Abstract
We consider the telegraph process with two velocities, a1>a2∈R, and two rates of reversal, λ1,λ2>0. We study some of its features with respect to the conditional probability measure where both the initial speed and the number of changes of direction are known. We exhibit a new proof by induction of the (conditional) probability law and a detailed study of the distribution of the motion at time t>0 conditioned on its position at a previous time 00, its maximum and its minimum up to that moment.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
