Record Statistics of Integrated Random Walks and the Random Acceleration Process

We address the theory of records for integrated random walks with finite variance. The long-time continuum limit these is a non-Markov process known as acceleration or integral Brownian motion. In this limit, renewal structure record cornerstone analysis its statistics. thus obtain analytical expressions several characteristics process, notably distribution total duration runs (sequences consecutive records), which analogue number walks. This result universal, i.e., independent details parent step lengths.