English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We investigate the effects of the resetting mechanism to the origin for arandom motion on the real line characterized by two alternating velocities$v_1$ and $v_2$. We assume that the sequences of random times concerning themotions along each velocity follow two independent geometric counting processesof intensity $\lambda$, and that the resetting times are Poissonian with rate$\xi >0$. Under these assumptions we obtain the probability laws of themodified telegraph process describing the position and the velocity of therunning particle. Our approach is based on the Markov property of the resettingtimes and on the knowledge of the distribution of the intertimes betweenconsecutive velocity changes. We obtain also the asymptotic distribution of theparticle position when (i) $\lambda$ tends to infinity, and (ii) the time goesto infinity. In the latter case the asymptotic distribution arises properly asan effect of the resetting mechanism. A quite different behavior is observed inthe two cases when $v_2<0<v_1$ and $0<v_2<v_1$. Furthermore, we focus on thedetermination of the moment-generating function and on the main moments of theprocess describing the particle position under reset. Finally, we analyse themean-square distance between the process subject to resets and the same processin absence of resets. Quite surprisingly, the lowest mean-square distance canbe found for $\xi =0$, for a positive $\xi$, or for $\xi\to +\infty$ dependingon the choice of the other parameters.

On the telegraph process driven by geometric counting process with Poisson-based resetting