Stochastic resetting by a random amplitude

Stochastic resetting, a diffusive process whose amplitude is "reset" to the origin at random times, vividly studied strategy optimize encounter dynamics, e.g., in chemical reactions. We here generalize resetting step by introducing amplitude, such that diffusing particle may be only partially reset towards trajectory origin, or even overshoot step. introduce different scenarios for random-amplitude stochastic and discuss resulting dynamics. Direct applications are geophysical layering (stratigraphy) as well population dynamics financial markets, generic search processes.