{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,27]],"date-time":"2026-04-27T10:24:54Z","timestamp":1777285494914,"version":"3.51.4"},"publisher-location":"New York, NY","reference-count":32,"publisher":"Springer New York","isbn-type":[{"value":"9781461449089","type":"print"},{"value":"9781461449096","type":"electronic"}],"license":[{"start":{"date-parts":[[2012,10,28]],"date-time":"2012-10-28T00:00:00Z","timestamp":1351382400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2012,10,28]],"date-time":"2012-10-28T00:00:00Z","timestamp":1351382400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013]]},"DOI":"10.1007\/978-1-4614-4909-6_10","type":"book-chapter","created":{"date-parts":[[2012,12,3]],"date-time":"2012-12-03T20:44:12Z","timestamp":1354567452000},"page":"209-225","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["A Fluid Introduction to Brownian Motion and Stochastic Integration"],"prefix":"10.1007","author":[{"given":"Vaidyanathan","family":"Ramaswami","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2012,10,28]]},"reference":[{"issue":"1","key":"10_CR1","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1081\/STM-120028392","volume":"20","author":"S Ahn","year":"2004","unstructured":"Ahn, S., Ramaswami, V.: Transient analysis of fluid flow models via stochastic coupling to a queue. Stoch. Models 20(1), 71\u2013101 (2004)","journal-title":"Stoch. Models"},{"issue":"1","key":"10_CR2","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1080\/15326340500481788","volume":"22","author":"S Ahn","year":"2006","unstructured":"Ahn, S., Ramaswami, V.: Transient analysis of fluid flow models via elementary level crossing argument. Stoch. Models 22(1), 129\u2013148 (2006)","journal-title":"Stoch. Models"},{"issue":"2","key":"10_CR3","doi-asserted-by":"publisher","first-page":"531","DOI":"10.1239\/jap\/1118777186","volume":"42","author":"S Ahn","year":"2005","unstructured":"Ahn, S., Ramaswami, V.: Efficient algorithms for transient analysis of stochastic fluid flow models. J. Appl. Probab. 42(2), 531\u2013549 (2005)","journal-title":"J. Appl. Probab."},{"key":"10_CR4","first-page":"207","volume":"55","author":"S Ahn","year":"2007","unstructured":"Ahn, S., Badescu, A.L, Ramaswami, V.: Transient analysis of finite buffer fluid flows and risk models with a dividend barrier. QUESTA 55, 207\u2013222 (2007)","journal-title":"QUESTA"},{"key":"10_CR5","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1080\/15326349508807329","volume":"11","author":"S Asmussen","year":"1995","unstructured":"Asmussen, S: Stationary distributions of fluid flow models with or without Brownian noise. Stoch. Models 11, 1\u201320 (1995)","journal-title":"Stoch. Models"},{"key":"10_CR6","doi-asserted-by":"publisher","DOI":"10.1002\/9780470316962","volume-title":"Convergence of Probability Measures","author":"P Billingsley","year":"1999","unstructured":"Billingsley, P.: Convergence of Probability Measures, 2nd edn. Wiley, New York (1999)","edition":"2"},{"key":"10_CR7","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-7652-0","volume-title":"Handbook of Brownian Motion - Facts and Formulae","author":"AN Borodin","year":"1996","unstructured":"Borodin, A.N., Salminen, P.: Handbook of Brownian Motion - Facts and Formulae. Birkh\u00e4user, Basel, Boston and Berlin (1996)"},{"key":"10_CR8","volume-title":"Probability","author":"L Breiman","year":"1968","unstructured":"Breiman, L.: Probability. Addison-Wesley, Reading, MA (1968)"},{"key":"10_CR9","volume-title":"A Course in Probability Theory","author":"KL Chung","year":"1968","unstructured":"Chung, K.L.: A Course in Probability Theory. Harcourt, Brace & World (1968)"},{"key":"10_CR10","first-page":"403","volume":"99","author":"Z Ciesielski","year":"1961","unstructured":"Ciesielski, Z.: H\u00f6lder conditions for realisations of Gaussian processes. Trans. Am. Math. Soc. 99, 403\u2013413 (1961)","journal-title":"Trans. Am. Math. Soc."},{"key":"10_CR11","first-page":"1","volume":"6","author":"M Donsker","year":"1951","unstructured":"Donsker, M.: An invariance principle for certain probability limit theorems. Mem. Am. Math. Soc. 6, 1\u201310 (1951)","journal-title":"Mem. Am. Math. Soc."},{"issue":"3","key":"10_CR12","doi-asserted-by":"publisher","first-page":"525","DOI":"10.1137\/S0036144500378302","volume":"43","author":"D Higham","year":"2001","unstructured":"Higham, D.: An algorithmic introduction to numerical simulation of stochastic differential equations. SIAM Rev. 43(3), 525\u2013546 (2001)","journal-title":"SIAM Rev."},{"key":"10_CR13","doi-asserted-by":"publisher","first-page":"519","DOI":"10.3792\/pia\/1195572786","volume":"20","author":"K It\u00f4","year":"1944","unstructured":"It\u00f4, K.: Stochastic Integral. Proc. Imper. Acad. Tokyo 20, 519\u2013524 (1944)","journal-title":"Stochastic Integral. Proc. Imper. Acad. Tokyo"},{"key":"10_CR14","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1007\/s10543-009-0211-6","volume":"49","author":"A Jentzen","year":"2009","unstructured":"Jentzen, A., Kloeden, P.E.: Pathwise Taylor schemes for random ordinary differential equations. BIT Numer. Math. 49, 113\u2013140 (2009)","journal-title":"BIT Numer. Math."},{"issue":"2","key":"10_CR15","first-page":"121","volume":"43","author":"R Karandikar","year":"1981","unstructured":"Karandikar, R.: Pathwise solutions of stochastic differential equations. Sankhya A 43(2), 121\u2013132 (1981)","journal-title":"Sankhya A"},{"key":"10_CR16","volume-title":"Brownian Motion and Stochastic Calculus","author":"I Karatzas","year":"1991","unstructured":"Karatzas, I., Shreve, S.E.: Brownian Motion and Stochastic Calculus. Springer, New York (1991)"},{"key":"10_CR17","volume-title":"Numerical Solution of Stochastic Differential Equations","author":"PE Kloeden","year":"1995","unstructured":"Kloeden, P.E., Platten, E.: Numerical Solution of Stochastic Differential Equations. Springer, Berlin (1995)"},{"key":"10_CR18","doi-asserted-by":"publisher","first-page":"746","DOI":"10.1239\/jap\/1091543423","volume":"41","author":"G Latouche","year":"2004","unstructured":"Latouche, G., Takine, T.: Markov renewal fluid queues. J. Appl. Probab. 41, 746\u2013757 (2004)","journal-title":"J. Appl. Probab."},{"issue":"3","key":"10_CR19","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1093\/rfs\/3.3.393","volume":"3","author":"D. Nelson","year":"1990","unstructured":"Nelson, D., Ramaswamy, K.: Simple binomial processes as diffusion approximations in financial models. Rev. Financ. Stud. 3, (3), 393\u2013430 (1990)","journal-title":"Rev. Financ. Stud."},{"key":"10_CR20","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-14394-6","volume-title":"Stochastic Differential Equations: An Introduction with Applications","author":"B \u00d8ksendal","year":"2003","unstructured":"\u00d8ksendal, B.: Stochastic Differential Equations: An Introduction with Applications. Springer, Berlin (2003)"},{"key":"10_CR21","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-02619-9","volume-title":"Stochastic Integration and Differential Equations","author":"P Protter","year":"1990","unstructured":"Protter, P.: Stochastic Integration and Differential Equations. Springer, New York (1990)"},{"key":"10_CR22","first-page":"1019","volume-title":"Teletraffic Engineering in a Competitive World. Proceedings of the 16th International Teletraffic Congress","author":"V Ramaswami","year":"1999","unstructured":"Ramaswami, V.: Matrix analytic methods for stochastic fluid flows. In: Smith, D., Key, P. (eds.) Teletraffic Engineering in a Competitive World. Proceedings of the 16th International Teletraffic Congress, pp. 1019\u20131030. Elsevier, New York (1999)"},{"key":"10_CR23","doi-asserted-by":"publisher","first-page":"497","DOI":"10.1007\/s11009-006-0426-9","volume":"8","author":"V Ramaswami","year":"2006","unstructured":"Ramaswami, V.: Passage times in fluid models with application to risk processes. Meth. Comput. Appl. Probab. 8, 497\u2013515 (2006)","journal-title":"Meth. Comput. Appl. Probab."},{"key":"10_CR24","volume-title":"Diffusions, Markov Processes and Martingales","author":"L.C.G. Rogers","year":"2000","unstructured":"Rogers, L.C.G., Williams, D.: Diffusions, Markov Processes and Martingales, vol. I. Cambridge University Press, Cambridge (2000)"},{"key":"10_CR25","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-22527-2","volume-title":"Stochastic Calculus for Finance","author":"SE Shreve","year":"2004","unstructured":"Shreve, S.E.: Stochastic Calculus for Finance, vol. 2. Continuous Time Models. Springer, Berlin (2004)"},{"key":"10_CR26","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1137\/1101022","volume":"1","author":"AV Skorohod","year":"1956","unstructured":"Skorohod, A.V.: Limit theorems for stochastic processes. Theor. Probab. Appl. 1, 261\u2013290 (1956)","journal-title":"Theor. Probab. Appl."},{"key":"10_CR27","volume-title":"The Encyclopedia of Actuarial Science","author":"MJ Steele","year":"2004","unstructured":"Steele, M.J.: Ito calculus. In: Teugels, J., Sundt, B. (eds.) The Encyclopedia of Actuarial Science. Wiley, New York (2004)"},{"issue":"2","key":"10_CR28","doi-asserted-by":"publisher","first-page":"362","DOI":"10.1137\/0304028","volume":"4","author":"RL Stratonovich","year":"1966","unstructured":"Stratonovich, R.L.: A new representation for stochastic integrals and equations. J. SIAM Contr. 4(2), 362\u2013371 (1966)","journal-title":"J. SIAM Contr."},{"key":"10_CR29","first-page":"101","volume":"41","author":"T Szabados","year":"2004","unstructured":"Szabados, T.: An elementary approach to the Wiener process and stochastic integrals. Stud. Sci. Math. Hung. 41, 101\u2013126 (2004)","journal-title":"Stud. Sci. Math. Hung."},{"key":"10_CR30","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1007\/s10959-007-0140-8","volume":"22","author":"T Szabados","year":"2009","unstructured":"Szabados, T., Sz\u00e9kely, B.: Stochastic integration based on simple, symmetric random walks. J. Theor. Probab. 22, 203\u2013219 (2009)","journal-title":"J. Theor. Probab."},{"key":"10_CR31","doi-asserted-by":"crossref","DOI":"10.1007\/b97479","volume-title":"Stochastic Process Limits","author":"W Whitt","year":"2002","unstructured":"Whitt, W.: Stochastic Process Limits. Springer, Berlin (2002)"},{"key":"10_CR32","doi-asserted-by":"crossref","first-page":"569","DOI":"10.24033\/bsmf.1071","volume":"52","author":"N Wiener","year":"1924","unstructured":"Wiener, N.: Un probl\u00e8me de probabilit\u00e9s \u00e9nombrables. Bull. Soc. Math. Fr. 52, 569\u2013568 (1924)","journal-title":"Bull. Soc. Math. Fr."}],"container-title":["Springer Proceedings in Mathematics & Statistics","Matrix-Analytic Methods in Stochastic Models"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-1-4614-4909-6_10","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,12]],"date-time":"2023-02-12T06:58:55Z","timestamp":1676185135000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-1-4614-4909-6_10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,10,28]]},"ISBN":["9781461449089","9781461449096"],"references-count":32,"URL":"https:\/\/doi.org\/10.1007\/978-1-4614-4909-6_10","relation":{},"ISSN":["2194-1009","2194-1017"],"issn-type":[{"value":"2194-1009","type":"print"},{"value":"2194-1017","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,10,28]]},"assertion":[{"value":"28 October 2012","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}