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Appl. Math."],"published-print":{"date-parts":[[2026,12]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>In this paper, a model mass-belt system with random friction is used to study the computational costs of modelling a problem with stick\u2013slip phenomena, stochastically. The objective is to assess the link between computational runtime and dynamical behaviour, specifically the duration and count of stick\/slip phases. Analysing the resulting multi-dimensional random vector (runtime, duration, count) is complex. This work investigates random variable transformations as a method to reduce analytical complexity by creating independent variables. We also use this approach to examine the influence of the integration method on the computational costs. Three different strategies to compute approximations to the system solutions are compared in terms of computational runtime and their relation with the duration and count of stick\/slip phases, the variables of greatest interest. One of the strategies used, for example, is Monte Carlo simulations coupled with a Multiple Scales analytical approximation. With this strategy, we find, for instance, that the number of stick\u2013slip transitions, rather than their duration, primarily dictates the predictive behaviour.<\/jats:p>","DOI":"10.1007\/s40314-026-03816-z","type":"journal-article","created":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T05:30:53Z","timestamp":1780551053000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Stochastic relation between runtime and dynamical behaviour of a system with uncertainties"],"prefix":"10.1007","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2092-7570","authenticated-orcid":false,"given":"H\u00e9ctor Eduardo","family":"Goicoechea Manuel","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3533-3054","authenticated-orcid":false,"given":"Roberta","family":"Lima","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2697-0019","authenticated-orcid":false,"given":"Rubens","family":"Sampaio","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,6,4]]},"reference":[{"key":"3816_CR1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmps.2020.104242","volume":"147","author":"G Albertini","year":"2021","unstructured":"Albertini G, Karrer S, Grigoriu MD, Kammer DS (2021) Stochastic properties of static friction. 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