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We study the dynamics of an overdamped Brownian particle subjected toPoissonian stochastic resetting in a nonthermal bath, characterized by aPoisson white noise and a Gaussian noise. Applying the renewal theory we findan exact analytical expression for the spatial distribution at the steadystate. Unlike the single exponential distribution as observed in the case of apurely thermal bath, the distribution is double exponential. Relaxation of thetransient spatial distributions to the stationary one, for the limiting casesof Poissonian rate, is investigated carefully. In addition, we study thefirst-arrival properties of the system in the presence of a delta-function sinkwith strength $\kappa$, where $\kappa=0$ and $\kappa=\infty$ correspond tofully nonreactive and fully reactive sinks, respectively. We explore the effectof two competitive mechanisms: the diffusive spread in the presence of twonoises and the increase in probability density around the initial position dueto stochastic resetting. We show that there exists an optimal resetting rate,which minimizes the mean first-arrival time (MFAT) to the sink for a givenvalue of the sink strength. We also explore the effect of the strength of thePoissonian noise on MFAT, in addition to sink strength. Our formalismgeneralizes the diffusion-limited reaction under resetting in a nonequilibriumbath and provides an efficient search strategy for a reactant to find a targetsite, relevant in a range of biophysical processes.

Stochastic resetting and first arrival subjected to Gaussian noise and Poisson white noise