Statistical fluctuations under resetting: rigorous results

In this paper we investigate the normal and large fluctuations of additive functionals associated with a stochastic process under general non-Poissonian resetting mechanism. Cumulative regenerative processes are very close to renewal-reward inherit most properties latter. Here review use classical law numbers central limit theorem for obtain same theorems resetting. Then, establish deviation principles these by illustrating applying theory that has been recently developed author. We discuss applications results positive occupation time, area, absolute area reset Brownian motion. While introducing advanced tools from renewal theory, demonstrate rich phenomenology accounting dynamical phase transitions emerges when one goes beyond Poissonian