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We develop a comprehensive framework for analyzing full record statistics,covering record counts $M(t_1), M(t_2), \ldots$, and their correspondingattainment times $T_{M(t_1)}, T_{M(t_2)}, \ldots$, as well as the intervalsuntil the next record. From this multiple-time distribution, we derive generalexpressions for various observables related to record dynamics, including theconditional number of records given the number observed at a previous time andthe conditional time required to reach the current record, given the occurrencetime of the previous one. Our formalism is exemplified by a variety ofstochastic processes, including biased nearest-neighbor random walks,asymmetric run-and-tumble dynamics, and random walks with stochastic resetting.

Full Record Statistics of 1d Random Walks