Active Brownian motion in two-dimensions under stochastic resetting

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 protocols : (I)
where both position and orientation of the particle are reset, (II) where only the position is reset,
and (III) where only the orientation is reset with a certain rate r. We show that in the first two cases
the ABP reaches a stationary state. Using a renewal approach, we calculate exactly the stationary
marginal position distributions in the limiting cases when the resetting rate r is much larger or
much smaller than the rotational diffusion constant D R of the ABP. We find that, in some cases,
for a large resetting rate, the position distribution diverges near the resetting point; the nature of
the divergence depends on the specific protocol. For the orientation resetting, there is no stationary
state, but the motion changes from a ballistic one at short-times to a diffusive one at late times.
We characterize the short-time non-Gaussian marginal position distributions using a perturbative
approach.