{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,18]],"date-time":"2025-11-18T20:50:24Z","timestamp":1763499024499},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2011,2,16]],"date-time":"2011-02-16T00:00:00Z","timestamp":1297814400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Period Math Hung"],"published-print":{"date-parts":[[2011,3]]},"DOI":"10.1007\/s10998-011-5075-2","type":"journal-article","created":{"date-parts":[[2011,2,16]],"date-time":"2011-02-16T22:53:04Z","timestamp":1297896784000},"page":"75-101","source":"Crossref","is-referenced-by-count":13,"title":["On hitting times of affine boundaries by reflecting Brownian motion and Bessel processes"],"prefix":"10.1007","volume":"62","author":[{"given":"Paavo","family":"Salminen","sequence":"first","affiliation":[]},{"given":"Marc","family":"Yor","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2011,2,16]]},"reference":[{"key":"5075_CR1","volume-title":"Mathematical functions","author":"M. Abramowitz","year":"1970","unstructured":"M. Abramowitz and I. Stegun, Mathematical functions, Dover publications, Inc., New York, 1970."},{"key":"5075_CR2","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/S0167-7152(02)00108-6","volume":"58","author":"M. Abundo","year":"2002","unstructured":"M. Abundo, Some conditional crossing results of Brownian motion over a piecewise-linear boundary, Statist. Probab. Lett., 58 (2002), 131\u2013145.","journal-title":"Statist. Probab. Lett."},{"key":"5075_CR3","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1016\/j.crma.2004.11.008","volume":"340","author":"L. Alili","year":"2005","unstructured":"L. Alili and P. Patie, On the first crossing times of a Brownian motion and a family of continuous curves, C. R. Math. Acad. Sci. Paris, 340 (2005), 225\u2013228.","journal-title":"C. R. Math. Acad. Sci. Paris"},{"key":"5075_CR4","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/s10959-009-0245-3","volume":"23","author":"L. Alili","year":"2010","unstructured":"L. Alili and P. Patie, Boundary crossing identities for diffusions having the time inversion property, J. Theoret. Probab., 23 (2010), 65\u201384.","journal-title":"J. Theoret. Probab."},{"key":"5075_CR5","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1090\/S0273-0979-01-00912-0","volume":"38","author":"Ph. Biane","year":"2001","unstructured":"Ph. Biane, J. Pitman and M. Yor, Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions, Bull. Amer. Math. Soc. (N.S.), 38 (2001), 435\u2013465.","journal-title":"Bull. Amer. Math. Soc. (N.S.)"},{"key":"5075_CR6","first-page":"23","volume":"111","author":"Ph. Biane","year":"1987","unstructured":"Ph. Biane and M. Yor, Valeurs principales associ\u00e9es aux temps locaux browniens, Bull. Sci. Math. (2), 111 (1987), 23\u2013101.","journal-title":"Bull. Sci. Math. (2)"},{"key":"5075_CR7","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-0348-8163-0","volume-title":"Handbook of Brownian motion \u2014 facts and formulae","author":"A. N. Borodin","year":"2002","unstructured":"A. N. Borodin and P. Salminen, Handbook of Brownian motion \u2014 facts and formulae, 2nd edition, Birkh\u00e4user, Basel, 2002.","edition":"2nd edition"},{"key":"5075_CR8","first-page":"9","volume-title":"Proc. 5th Berkeley Symp. Math. Stat. Probab. Vol. 2","author":"L. Breiman","year":"1967","unstructured":"L. Breiman, First exit times from a square root boundary, Proc. 5th Berkeley Symp. Math. Stat. Probab. Vol. 2, University of California, Berkeley, 1967, 9\u201316."},{"key":"5075_CR9","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1007\/BF02385832","volume":"14","author":"K. L. Chung","year":"1976","unstructured":"K. L. Chung, Excursions in Brownian motion, Ark. Mat., 14 (1976), 155\u2013177.","journal-title":"Ark. Mat."},{"key":"5075_CR10","first-page":"492","volume":"32","author":"D. M. Cifarelli","year":"1973","unstructured":"D. M. Cifarelli and E. Regazzini, Sugli stimatori non distorti a varianza minima di una classe di funzioni di probabilit\u00e0 troncate, Giorn. Econom. Ann. Econom. (N.S.), 32 (1973), 492\u2013501.","journal-title":"Giorn. Econom. Ann. Econom. (N.S.)"},{"key":"5075_CR11","doi-asserted-by":"crossref","first-page":"2197","DOI":"10.1080\/03610928108828182","volume":"10","author":"D. M. Delong","year":"1981","unstructured":"D. M. Delong, Crossing probabilities for a square root boundary by a Bessel process, Comm. Statist. A\u2014Theory Methods, 10 (1981), 2197\u20132213.","journal-title":"Comm. Statist. A\u2014Theory Methods"},{"key":"5075_CR12","first-page":"1699","volume":"12","author":"D. M. Delong","year":"1983","unstructured":"D. M. Delong, Erratum: \u201cCrossing probabilities for a square root boundary by a Bessel process\u201d. [Comm. Statist. A\u2014Theory Methods, 10(1981), 2197\u20132213; MR 82i:62119], Comm. Statist. A\u2014Theory Methods, 12 (1983), 1699.","journal-title":"Comm. Statist. A\u2014Theory Methods"},{"key":"5075_CR13","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1214\/aoms\/1177729991","volume":"20","author":"J. L. Doob","year":"1949","unstructured":"J. L. Doob, Heuristic approach to the Kolmogorov-Smirnov theorems, Ann. Math. Statistics, 20 (1949), 393\u2013403.","journal-title":"Ann. Math. Statistics"},{"key":"5075_CR14","doi-asserted-by":"crossref","first-page":"431","DOI":"10.2307\/3212169","volume":"8","author":"J. Durbin","year":"1971","unstructured":"J. Durbin, Boundary-crossing probabilities for the Brownian motion and Poisson processes and techniques for computing the power of the Kolmogorov-Smirnov test, J. Appl. Probability, 8 (1971), 431\u2013453.","journal-title":"J. Appl. Probability"},{"key":"5075_CR15","doi-asserted-by":"crossref","first-page":"291","DOI":"10.2307\/3214567","volume":"29","author":"J. Durbin","year":"1992","unstructured":"J. Durbin, The first passage density of a Brownian motion process to a curved boundary, J. Appl. Probab., 29 (1992), 291\u2013304.","journal-title":"J. Appl. Probab."},{"key":"5075_CR16","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1214\/aop\/1176995896","volume":"5","author":"R. Durrett","year":"1977","unstructured":"R. Durrett and D.I. Iglehart, Functionals of Brownian meander and Brownian excursion, Ann. Probability, 5 (1977), 130\u2013135.","journal-title":"Ann. Probability"},{"key":"5075_CR17","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1214\/aoms\/1177729589","volume":"22","author":"W. Feller","year":"1951","unstructured":"W. Feller, The asymptotic distribution of the range of sums of independent random variables, Ann. Math. Statistics, 22 (1951), 427\u2013432.","journal-title":"Ann. Math. Statistics"},{"key":"5075_CR18","volume-title":"An introduction to probability theory and its applications, Vol. II.","author":"W. Feller","year":"1971","unstructured":"W. Feller, An introduction to probability theory and its applications, Vol. II., Second edition, John Wiley & Sons Inc., New York, 1971.","edition":"Second edition"},{"key":"5075_CR19","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1007\/BF00343738","volume":"81","author":"P. Groeneboom","year":"1989","unstructured":"P. Groeneboom, Brownian motion with a parabolic drift and Airy functions, Probab. Theory Related Fields, 81 (1989), 79\u2013109.","journal-title":"Probab. Theory Related Fields"},{"key":"5075_CR20","doi-asserted-by":"crossref","first-page":"371","DOI":"10.2307\/3212843","volume":"13","author":"D. Kennedy","year":"1976","unstructured":"D. Kennedy, The distribution of the maximum Brownian excursion, J. Appl. Probability, 13 (1976), 371\u2013376.","journal-title":"J. Appl. Probability"},{"key":"5075_CR21","series-title":"Lecture Notes in Statistics","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4615-6569-7","volume-title":"Boundary crossing of Brownian motion","author":"H. R. Lerche","year":"1986","unstructured":"H. R. Lerche, Boundary crossing of Brownian motion, Lecture Notes in Statistics 40, Springer-Verlag, Berlin, 1986."},{"key":"5075_CR22","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1239\/jap\/1032265215","volume":"35","author":"A. Martin-L\u00f6f","year":"1998","unstructured":"A. Martin-L\u00f6f, The final size of a nearly critical epidemic, and the first passage time of a Wiener process to a parabolic barrier, J. Appl. Probab., 35 (1998), 671\u2013682.","journal-title":"J. Appl. Probab."},{"key":"5075_CR23","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1007\/BF00532494","volume":"1","author":"H. Mckean","year":"1963","unstructured":"H. Mckean, Excursions of a non-singular diffusion, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 1 (1963), 230\u2013239.","journal-title":"Z. Wahrscheinlichkeitstheorie und Verw. Gebiete"},{"key":"5075_CR24","series-title":"Lectures in Mathematics ETH Z\u00fcrich","volume-title":"Optimal stopping and free-boundary problems","author":"G. Peskir","year":"2006","unstructured":"G. Peskir and A.N. Shiryaev, Optimal stopping and free-boundary problems, Lectures in Mathematics ETH Z\u00fcrich, Birkh\u00e4user Verlag, Basel, 2006."},{"key":"5075_CR25","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1007\/BFb0088732","volume-title":"Stochastic Integrals","author":"J. Pitman","year":"1981","unstructured":"J. Pitman and M. Yor, Bessel processes and infinitely divisible laws, Stochastic Integrals (ed.: D. Williams), Lecture Notes in Mathematics 851, Springer Verlag, Heidelberg \u2014 Berlin, 1981, 285\u2013370."},{"key":"5075_CR26","doi-asserted-by":"crossref","unstructured":"J. Pitman and M. Yor, The law of the maximum of a Bessel bridge, Electron. J. Probab., 4 (1999), 35 pp. (electronic).","DOI":"10.1214\/EJP.v4-52"},{"key":"5075_CR27","doi-asserted-by":"crossref","first-page":"292","DOI":"10.4153\/CJM-2003-014-x","volume":"55","author":"J. Pitman","year":"2003","unstructured":"J. Pitman and M. Yor, Infinitely divisible laws associated with hyperbolic functions, Canad. J. Math., 55 (2003), 292\u2013330.","journal-title":"Canad. J. Math."},{"key":"5075_CR28","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-06400-9","volume-title":"Continuous martingales and Brownian motion","author":"D. Revuz","year":"1999","unstructured":"D. Revuz and M. Yor, Continuous martingales and Brownian motion, 3rd edition, Springer Verlag, Berlin, 1999.","edition":"3rd edition"},{"key":"5075_CR29","doi-asserted-by":"crossref","first-page":"411","DOI":"10.2307\/1427397","volume":"20","author":"P. Salminen","year":"1988","unstructured":"P. Salminen, On the first hitting time and the last exit time for a Brownian motion to\/from a moving boundary, Adv. in Appl. Probab., 20 (1988), 411\u2013426.","journal-title":"Adv. in Appl. Probab."},{"key":"5075_CR30","first-page":"251","volume":"33","author":"P. Salminen","year":"1997","unstructured":"P. Salminen, On last exit decomposition of linear diffusions, Studia Sci. Math. Hungar., 33 (1997), 251\u2013262.","journal-title":"Studia Sci. Math. Hungar."},{"key":"5075_CR31","unstructured":"P. Salminen and M. Yor, On some probabilistic occurrences of the Poisson summation formula, in preparation."},{"key":"5075_CR32","doi-asserted-by":"crossref","first-page":"448","DOI":"10.2307\/3214581","volume":"29","author":"T. H. Scheike","year":"1992","unstructured":"T. H. Scheike, A boundary-crossing result for Brownian motion, J. Appl. Probab., 29 (1992), 448\u2013453.","journal-title":"J. Appl. Probab."},{"key":"5075_CR33","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1214\/aop\/1176993926","volume":"10","author":"L. A. Shepp","year":"1982","unstructured":"L. A. Shepp, On the integral of the absolute value of the pinned Wiener process, Ann. Probab., 10 (1982), 234\u2013239.","journal-title":"Ann. Probab."},{"key":"5075_CR34","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1007\/BF00736006","volume":"27","author":"T. Shiga","year":"1973","unstructured":"T. Shiga and S. Watanabe, Bessel diffusions as a one-parameter family of diffusion processes, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 27 (1973), 37\u201346.","journal-title":"Z. Wahrscheinlichkeitstheorie und Verw. Gebiete"},{"key":"5075_CR35","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1214\/aop\/1176995155","volume":"7","author":"W. Vervaat","year":"1979","unstructured":"W. Vervaat, A relation between Brownian bridge and Brownian excursion, Ann. Probab., 7 (1979), 143\u2013149.","journal-title":"Ann. Probab."},{"key":"5075_CR36","doi-asserted-by":"crossref","first-page":"738","DOI":"10.1112\/plms\/s3-28.4.738","volume":"28","author":"D. Williams","year":"1974","unstructured":"D. Williams, Path decompositions and continuity of local time for one-dimensional diffusions, Proc. London Math. Soc., 28 (1974), 738\u2013768.","journal-title":"Proc. London Math. Soc."},{"key":"5075_CR37","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1007\/BFb0099124","volume-title":"Stochastic analysis and applications","author":"M. Yor","year":"1984","unstructured":"M. Yor, On square-root boundaries for Bessel processes, and pole-seeking Brownian motion, Stochastic analysis and applications (Swansea, 1983), Lecture Notes in Mathematics 1095, Springer Verlag, Berlin, 1984, 100\u2013107."}],"container-title":["Periodica Mathematica Hungarica"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-011-5075-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10998-011-5075-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-011-5075-2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,8]],"date-time":"2019-06-08T15:59:16Z","timestamp":1560009556000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10998-011-5075-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,2,16]]},"references-count":37,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2011,3]]}},"alternative-id":["5075"],"URL":"https:\/\/doi.org\/10.1007\/s10998-011-5075-2","relation":{},"ISSN":["0031-5303","1588-2829"],"issn-type":[{"value":"0031-5303","type":"print"},{"value":"1588-2829","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,2,16]]}}}