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We determine the full distribution and moments of the first passage time fora wide class of stochastic search processes in the limit of frequent stochasticresetting. Our results apply to any system whose short-time behavior of thesearch process without resetting can be estimated. In addition to the typicalcase of exponentially distributed resetting times, we prove our results for awide array of resetting time distributions. We illustrate our results inseveral examples and show that the errors of our approximations vanishexponentially fast in typical scenarios of diffusive search.

First passage times under frequent stochastic resetting