{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,13]],"date-time":"2025-06-13T04:07:54Z","timestamp":1749787674157,"version":"3.41.0"},"reference-count":38,"publisher":"American Mathematical Society (AMS)","issue":"355","license":[{"start":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T00:00:00Z","timestamp":1769126400000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>The Wiener-Hopf factorization, which is characterized as special solutions to a pair of nonlinear matrix equations, plays a crucial role in analysis of the Markov-modulated Brownian motion (<sc>mmbm<\/sc>). This paper deals with the general case where the diffusion coefficients are nonzero for some but not all states of the governing Markov chain. Based on a novel regrouping of the unknowns in the Wiener-Hopf factorization and a new form for the initialization phase, a doubling algorithm is proposed to solve the pair of nonlinear matrix equations simultaneously. With the parameters of the <sc>mmbm<\/sc> as input, this doubling algorithm is implemented in a subtraction-free manner to compute the Wiener-Hopf factorization to high entrywise relative accuracy. Numerical examples are presented to demonstrate and confirm our claims.<\/p>","DOI":"10.1090\/mcom\/4055","type":"journal-article","created":{"date-parts":[[2024,12,3]],"date-time":"2024-12-03T17:36:40Z","timestamp":1733247400000},"page":"2367-2408","source":"Crossref","is-referenced-by-count":1,"title":["Efficient computation of Wiener-Hopf factorization of Markov-modulated Brownian motion"],"prefix":"10.1090","volume":"94","author":[{"given":"Changli","family":"Liu","sequence":"first","affiliation":[]},{"given":"Jungong","family":"Xue","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2025,1,23]]},"reference":[{"issue":"3","key":"1","doi-asserted-by":"publisher","first-page":"448","DOI":"10.1016\/j.jkss.2014.12.005","article-title":"Alternative fluid approximation approach for the steady-state distribution of the two-sided reflected Markov modulated Brownian motion and its computation","volume":"44","author":"Ahn, Soohan","year":"2015","journal-title":"J. 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