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Biol."],"published-print":{"date-parts":[[2026,9]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    We prove a large deviation principle for piecewise deterministic Markov processes (PDMPs). This is an asymptotic estimate for the probability of a trajectory in the large size limit. Explicit Euler\u2013Lagrange equations are determined for computing optimal first-hitting-time trajectories. The results are applied to a model of stochastic calcium dynamics. It is widely conjectured that the mechanism of calcium puff generation is a multiscale process: with microscopic stochastic fluctuations in the opening and closing of individual channels generating cell-wide waves via the diffusion of calcium and other signaling molecules. We model this system as a PDMP, with\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$N\\gg 1$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mi>N<\/mml:mi>\n                            <mml:mo>\u226b<\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    stochastic calcium channels that are coupled via the ambient calcium concentration. We employ the large deviations theory to estimate the probability of cell-wide calcium waves being produced through microscopic stochasticity.\n                  <\/jats:p>","DOI":"10.1007\/s00285-026-02446-7","type":"journal-article","created":{"date-parts":[[2026,8,28]],"date-time":"2026-08-28T05:21:28Z","timestamp":1787894488000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Large deviations of piecewise-deterministic Markov processes with application to stochastic calcium waves"],"prefix":"10.1007","volume":"93","author":[{"given":"Gaetan","family":"Barbet","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5577-9846","authenticated-orcid":false,"given":"James","family":"MacLaurin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Moshe","family":"Silverstein","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pedro","family":"Vilanova","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,8,28]]},"reference":[{"key":"2446_CR1","doi-asserted-by":"publisher","first-page":"1821","DOI":"10.1214\/17-AAP1344","volume":"28","author":"A Agazzi","year":"2018","unstructured":"Agazzi A, Dembo A, Eckmann JP (2018) Large deviations theory for Markov jump models of chemical reaction networks. 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