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 …

Stochastic resetting is prevalent in natural and man-made systems, giving rise to a long
series of nonequilibrium phenomena. Diffusion with stochastic resetting serves as a …

The remaining travel time of a plane shortens with every minute that passes from its
departure, and a flame diminishes a candle with every second it burns. Such everyday …

How do near-bankruptcy events in the past affect the dynamics of stock-market prices in the
future? Specifically, what are the long-time properties of a time-local exponential growth of …

Motion under stochastic resetting serves to model a myriad of processes in physics and
beyond, but in most cases studied to date resetting to the origin was assumed to take zero …

Markov processes restarted or reset at random times to a fixed state or region in space have
been actively studied recently in connection with random searches, foraging, and population …

For the M/M/1 queue in the presence of catastrophes the transition probabilities, densities of
the busy period and of the catastrophe waiting time are determined. A heavy-traffic …

What determines the average length of a queue, which stretches in front of a service station?
The answer to this question clearly depends on the average rate at which jobs arrive at the …

The arrival of a negative customer to a queueing system causes one ordinary customer to be
removed (or killed) if any is present. The arrival of a disaster, on the other hand, kills all the …

A transient solution is obtained analytically using continued fractions for the system size in
an M/M/1 queueing system with catastrophes, server failures and non-zero repair time. The …