The Kolmogorov-Arnold stochasticity parameter technique is applied for the first time to the study of cancer genome sequencing, to reveal mutations. Using data generated by next-generation sequencing technologies, we have analysed the exome sequences of brain tumour patients with matched tumour and normal blood. We show that mutations contained in sequencing data can be revealed using this technique, thus providing a new methodology for determining subsequences of given length containing mutations, i.e. its value differs from those of subsequences without mutations. A potential application for this technique involves simplifying the procedure of finding segments with mutations, speeding up genomic research and accelerating its implementation in clinical diagnostics. Moreover, the prediction of a mutation associated with a family of frequent mutations in numerous types of cancers based purely on the value of the Kolmogorov function indicates that this applied marker may recognize genomic sequences that are in extremely low abundance and can be used in revealing new types of mutations.