In this topical review we consider stochastic processes under resetting, which have attracted
a lot of attention in recent years. We begin with the simple example of a diffusive particle …

Full article: Martingales for physicists: a treatise on stochastic thermodynamics and beyond
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We consider a particle undergoing run and tumble dynamics, in which its velocity
stochastically reverses, in one dimension. We study the addition of a Poissonian resetting …

We study the dynamics of a one-dimensional run-and-tumble particle subjected to confining
potentials of the type V (x)= α| x| p, with p> 0. The noise that drives the particle dynamics is …

We study the position distribution of an active Brownian particle (ABP) in the presence of
stochastic resetting in two spatial dimensions. We consider three different resetting …

We provide an analytical solution for the time-dependent Fokker-Planck equation for a two-
dimensional active Brownian particle trapped in an isotropic harmonic potential. Using the …

We consider an overdamped run-and-tumble particle in two dimensions, with self-propulsion
in an orientation that stochastically rotates by 90∘ at a constant rate, clockwise or …

We consider an active run-and-tumble particle (RTP) in d dimensions and compute exactly
the probability S (t) that the x component of the position of the RTP does not change sign up …

We study the dynamics of a single active Brownian particle (ABP) in two spatial dimensions.
The ABP has an intrinsic timescale DR− 1 set by the rotational diffusion constant DR. We …

Abstract Run-and-tumble (RnT) motion is an example of active motility where particles move
at constant speed and change direction at random times. In this work we study RnT motion …