Publications of Allan Gut

Ph D thesis

• On the moments and limit distributions of some first passage times. Department of Mathematics, Uppsala University, Uppsala, 1972.

Books

• (with Klaus Schmidt). Amarts and set function processes. Lecture Notes in Mathematics 1042. Springer-Verlag, Berlin, 1983.
• Stopped Random Walks. Limit Theorems and Applications. Springer-Verlag, New York, 1988.
• An Intermediate Course in Probability. Springer-Verlag, New York, 1995. Misprints and corrections; pdf-file.
• Sant eller sannolikt. Norstedts förlag, 2002. PAN pocket, 2004.
• Probability: A Graduate Course. Springer-Verlag, New York, 2005. Misprints and corrections; pdf-file. Corr. 2nd printing, 2007. Misprints; pdf-file.
• Konsten att räkna. Norstedts förlag, 2007.
• Stopped Random Walks. Limit Theorems and Applications, 2nd ed. Springer-Verlag, New York, 2009.
• An Intermediate Course in Probability, 2nd ed. Springer-Verlag, New York, 2009. Misprints and corrections; pdf-file.
• Probability: A Graduate Course, 2nd ed. Springer-Verlag, New York, 2013. Misprints; pdf-file. Misprints and corrections; thanks to Andreas Schäfer.
• 100 procent finns inte. Fri Tanke förlag, 2015.

Published articles

• On the moments and limit distributions of some first passage times. Ann. Probab. 2 (1974), 277-308.
• On the moments of some first passage times for sums of dependent random variables. Stoch. Proc. Appl. 2 (1974), 115-126.
• A functional central limit theorem connected with extended renewal theory. Z. Wahrsch. verw. Geb. 27 (1973), 123-129.
• On convergence in r-mean of some first passage times and randomly indexed partial sums. Ann. Probab. 2 (1974), 321-323.
• Weak convergence and first passage times. J. of Appl. Probab. 12 (1975), 324-332.
• On a.s. and r-mean convergence of random processes with an application to first passage times. Z. Wahrsch. verw. Geb. 31 (1975), 333-341.
• Convergence of reversed martingales with multidimensional indices. Duke Math. J. 43 (1976), 269-275.
• Marcinkiewicz laws and convergence rates in the law of large numbers for random variables with multidimensional indices. Ann. Probab. 6 (1978), 469-482.
• Convergence rates for probabilities of moderate deviations for sums of random variables with multidimensional indices. Ann. Probab. 8 (1980), 298-313.
• Moments of the maximum of normed partial sums of random variables with multidimensional indices. Z. Wahrsch. verw. Geb. 46 (1979), 205-220.
• On the integrability of sup|S_n/n| for subsequences. Ann. Probab. 7 (1979), 1059-1065.
• A contribution to the theory of asymptotic martingales. Glasgow Math. J . 23 (1982), 177-186.
• (with P. Ahlberg). On the theory of chromatography based upon renewal theory and a central limit theorem for randomly indexed partial sums of random variables. Chemica Scripta 18 (1981), 248-255.
• An introduction to the theory of asymptotic martingales. In: Amarts and set function processes. Lecture Notes in Mathematics 1042, 1-49 and (with K.D. Schmidt), 237-258. Springer-Verlag, Berlin, 1983.
• (with S. Janson). The limiting behaviour of certain stopped sums and some applications. Scand. J. Statist. 10 (1983), 281-292 .
• A central limit theorem for certain stopped sums and some applications. Proc. 7th Brasov Conf. on Prob. Theory, 165-172. Bucuresti, 1984.
• Complete convergence and convergence rates for randomly indexed partial sums with an application to some first passage times. Acta Math. Acad. Sci. Hungar. 42 (1983), 225-232; Correction, ibid. 45 (1985), 235-236.
• Strong laws for independent identically distributed random variables indexed by a sector. Ann. Probab. 11 (1983), 569-577.
• Renewal theory and ladder variables. In: Probability and Mathematical Statistics. Essays in honour of Carl-Gustav Esseen. (Eds. A. Gut and L. Holst ), 25-39. Uppsala 1983.
• The law of the iterated logarithm for subsequences. Probab. Math. Statist. VII (1986), 27-58.
• On the law of the iterated logarithm for randomly indexed partial sums with two applications. Studia Sci. Math. Hungar. 20 (1985), 63-69.
• On complete convergence in the law of large numbers for subsequences. Ann. Probab. 13 (1985), 1286-1291.
• (with L. Holst ). On the waiting time in a roulette game. Uppsala 1983.
• (with L. Holst ). On the waiting time in a generalized roulette game. Statist. Probab. Lett. 2 (1984), 229-239.
• (with J. Hüsler). The rate of growth of sample maxima with multidimensional indices. Bern 1984.
• (with I. Torrång, L. Holm-Rutili, K.J. Öbrink). A probabilistic approach for evaluating a technique for an indirect monitoring of the capillary blood flow to the gastric parietal cells. Bull. Math. Biol. 49 (1987), 171-185.
• (with S. Janson). Converse results for existence of moments and uniform integrability for stopped random walks. Ann. Probab. 14 (1986), 1296-1317.
• Converse results for existence of moments for stopped random walks. Proc. 1st World Congress of the Bernoulli Society (Tashkent, 1986), Vol. 2, 429-433, VNU Sci. Press, Utrecht, 1987.
• Limit points of sample maxima. Statist. Probab. Lett. 9 (1990), 331-336.
• Limit theorems for record times. Proc. 5th Vilnius Conf. on Prob. Theory and Math. Stat. Vol. 1, 490-503. Vilnius, Lithuania, Utrecht, The Netherlands, 1990.
• Convergence rates for record times and the associated counting process. Stoch. Proc. Appl. 36 (1990), 135-151.
• On the growth rate of slowly varying functions. Acta Math. Vietnam. 19 (1994), 13-24.
• First passage times of perturbed random walks. Sequential Anal. 11 (1992), 149-179.
• Cumulative shock models. Adv. in Appl. Probab. 22 (1990), 504-507.
• Anscombe laws of the iterated logarithm. Probab. Math. Statist. 12 (1991), 127-137.
• Complete convergence for arrays. Period. Math. Hungar. 25 (1992), 51-75.
• The weak law of large numbers for arrays. Statist. Probab. Lett. 14 (1992), 49-52.
• Complete convergence and Cesàro summation for i.i.d. random variables. Probab. Th. Rel. Fields 97 (1993), 169-178.
• Stopped Lévy processes with applications to first passage times. Statist. Probab. Lett. 28 (1996), 345-352.
• Complete convergence. Asymptotic Statistics. Proc. 5th Prague Symp., 237-247. Physica-Verlag, Springer, Heidelberg 1994.
• (with R. Schwabe). On the law of the iterated logarithm for rapidly increasing subsequences. Math. Nachr. 178 (1996), 309-320.
• Stopped two-dimensional perturbed random walks and Lévy processes. Statist. Probab. Lett. 35 (1997), 317-325.
• (with R. Schwabe). Some properties of multiple decisions following a sequential test. Sequential Anal. 15 (1996), 299-310.
• (with G. Alsmeyer). Limit theorems for stopped functionals of Markov renewal processes. Ann. Inst. Statist. Math 51 (1999), 369-382.
• (with R. Schwabe). Some remarks on repeated significance tests for linear contrasts. J. Statist. Plann. Inference 82 (1999), 25-34.
• (with O. Klesov and J. Steinebach). Equivalences in strong limit theorems for renewal counting processes. Statist. Probab. Lett. 35 (1997), 381-394.
• (with M. Peligrad). Almost sure results for a class of dependent random variables. J. Theor. Probab. 12 (1999), 87-104.
• (with A. Spataru). Precise asymptotics in the Baum-Katz and Davis laws of large numbers. J. Math. Anal. Appl. 248 (2000), 233-246.
• (with A. Spataru). Precise asymptotics in the law of the iterated logarithm. Ann. Probab. 28 (2000), 1870-1883.
• (with J. Hüsler). Extreme shock models. EXTREMES 2 (1999), 295-307.
• (with S. Janson). Tightness and weak convergence for jump processes. Statist. Probab. Lett. 52 (2001), 101-107.
• (with A. Spataru). Precise asymptotics in some strong limit theorems for multidimensionally indexed random variables. J. Multivariate Anal. 86 (2003), 398-422.
• Convergence rates in the central limit theorem for multidimensionally indexed random variables. Studia Sci. Math. Hungar. 37 (2001), 401-418.
• Mixed shock models. BERNOULLI 7 (2001), 541-555.
• (with Josef Steinebach). Truncated sequential change-point detection based on renewal counting processes. Scand. J. Statist 29 (2002), 693-719.
• On the moment problem. BERNOULLI 8 (2002), 407-421.
• (with Valentin V. Petrov). Generalized laws of the iterated logarithm. Commun. Statist. -- Theory Meth. 32 (2003), 1685-1693.
• (with Josef Steinebach). Convergence rates and precise asymptotics for renewal counting processes and some first passage times. Proceedings of the International Conference on Asymptotic Methods in Stochastics, May 23-25, 2002, Carleton University Ottawa. Fields Institute Communications 44 (2004), 205-227.
• Precise asymptotics for record times and the associated counting process. Stoch. Proc. Appl. 101 (2002), 233-239.
• On the moment problem for sums of a random number of random variables. J. of Appl. Probab. 40 (2003), 797-802.
• (with Josef Steinebach). EWMA charts for detecting a change-point in the drift of a stochastic process. Sequential Anal. 23 (2004), 195-237.
• An extension of the Kolmogorov-Feller weak law of large numbers with an application to the St Petersburg game. J. Theor. Probab. 17 (2004), 769-779.
• (with J. Hüsler). Realistic variation of shock models. Statist. Probab. Lett. 74 (2005), 187-204.
• Sant eller sannolikt i vardagslivet. Konferanserapport: Popularisering av matematikk, November 15-18, 2003, Trondheim, (2004), 59-68.
• Some remarks on the Riemann zeta distribution. Rev. Roumaine Math. Pures et Appl. 51 (2006), 205-217.
• Gnedenko-Raikov's theorem, central limit theory, and the weak law of large numbers. Statist. Probab. Lett. 76 (2006), 1935-1939.
• (with Josef Steinebach). A two-step sequential procedure for detecting an epidemic change. EXTREMES 8 (2005), 311-326.
• Beurling, CGE och CGS. Jubileumsskrift Arne Beurling 100 år. U.U.D.M. Report 2007:34, Department of Mathematics, Uppsala University (2007), 15-21.
• (with Ulrich Stadtmüller). Laws of the single logarithm for delayed sums of random fields. BERNOULLI 14 (2008), 249-276.
• (with Josef Steinebach). On sequential change-point detection. Proceedings of the 2008 International Workshop on Applied Probability, July 7-10 2008, Université de Technologie de Compiègne, France. (2008).
• (with Ulrich Stadtmüller). Laws of the single logarithm for delayed sums of random fields II. J. Math. Anal. Appl. 346 (2008), 403-414.
• (with Josef Steinebach). Truncated sequential change-point detection based on renewal counting processes II. J. Statist. Plann. Inference 139 (2009), 1921-1936.
• (with Fredrik Jonsson and Ulrich Stadtmüller). Between the LIL and the LSL. BERNOULLI 16 (2010), 1-22.
• (with Nitis Mukhopadhyay). On asymptotic and strict monotonicity of a sharper lower bound for Student's t percentiles. Methodol. Comput. Appl. Probab. 12 (2010), 647-657.
• (with Ulrich Stadtmüller). An asymmetric Marcinkiewicz-Zygmund LLN for random fields. Statist. Probab. Lett. 79 (2009), 1016-1020.
• (with Ulrich Stadtmüller). Cesàro summation for random fields. J. Theor. Probab. 23 (2010), 715-728.
• (with Josef Steinebach). Sequential change-point analysis for renewal counting processes. Proc. Sixth St. Petersburg Workshop on Simulation, (Eds. S.M. Ermakov, V.B. Melas and A.N. Pepelyshev), St. Petersburg, Russia, June 28 - July 4, 2009, VVM com Ltd., St. Petersburg, 2009, 667-672.
• (with J. Hüsler). Shock models. Advances in degradation modeling, Stat. Ind. Technol., Birkhäuser Boston, Inc., Boston, MA, (2010), 59-76.
• (with Josef Steinebach). Sequential detection of change-points in counting processes. Proceedings of Second International Workshop in Sequential Methodologies, June 15-17 2009, Université de Technologie de Troyes, France (2009).
• (with Ulrich Stadtmüller). On the LSL for random fields. J. Theor. Probab. 24 (2011), 422-449.
• (with Josef Steinebach). Asymptotics for increments of stopped renewal processes. Statist. Probab. Lett. 80 (2010), 558-565.
• (with Ulrich Stadtmüller). On the strong law of large numbers for delayed sums and random fields. Acta Math. Hungar. 129 (2010), 182-203.
• Limit theorems for a generalized St. Petersburg game. J. Appl. Probab. 47 (2010), 752-760. Correction; pdf-file.
• Renewal theory with a trend. Statist. Probab. Lett. 81 (2011), 1292-1299.
• (with Ulrich Stadtmüller). An intermediate Baum-Katz theorem Statist. Probab. Lett. 81 (2011), 1486-1492.
• (with Ulrich Stadtmüller). On the Hsu-Robbins-Erdös-Spitzer-Baum-Katz theorem for random fields. J. Math. Anal. Appl. 387 (2012), 447-463.
• (with Josef Steinebach). Convergence rates in precise asymptotics. J. Math. Anal. Appl. 390 (2012), 1-14. Correction; pdf-file.
• Anscombe's theorem 60 years later. Sequential Anal. 31 (2012), 368-396.
• (with Josef Steinebach). Convergence rates in precise asymptotics II. Annales Univ. Sci. Budapest., Sect. Comp. 39 (2013), 95-110.
• (with Josef Steinebach). Precise asymptotics---a general approach. Acta Math. Hungar. 138 (2013), 365-385.
• Strong limit theorems for random fields. Proceedings of the Conference on Stochastic Models and their Applications, August 22 - 24, 2011, University of Debrecen, Hungary. Annales Mathematicae et Informaticae 39 (2012), 125-157.
• (with Ulrich Stadtmüller). Records in subsets of a random field. Statist. Probab. Lett. 83 (2013), 689-699.
• (with Anders Martin Löf). Generalized St. Petersburg games revisited. arXiv:1506.09015.
• Some remarks on distributed sensing with costs. Probab. Engr. Inform. Sci. 28 (2014), 271-277.
• The gambler's ruin with delays. Statist. Probab. Lett. 83 (2013), 2549-2552.
• On convergence of randomly indexed sequences; a counterexample based on the St. Petersburg game. Statist. Probab. Lett. 87 (2014), 105-107.
• (with Anders Martin Löf). A maxtrimmed St. Petersburg game. J. Theor. Probab. 29 (2016), 277-291.
• (with Anders Martin Löf). Extreme-trimmed St. Petersburg games. Statist. Probab. Lett. 96 (2015), 341-345.
• (with Ulrich Stadtmüller). Limit theorems for counting processes based on records and extremes . Extremes 20 (2017), 33-52.
• Stora talens lag i vardagen. Ann. Acad. Reg. Sci. Upsaliensis 41 (2015-2016) (2017), 47-62.
• (with Ulrich Stadtmüller). Complete convergence for arrays and the law of the single logarithm. Bull. Aust. Math. Soc. 96 (2017), 333-344..
• (with Ulrich Stadtmüller). Strong laws for sequences in the vicinity of the LIL. Statist. Probab. Lett 122 (2017), 63-72.
• (with Ulrich Stadtmüller). Almost sure limit behavior of Cesàro sums with small order. Acta Math. Hungar. 151 (2017), 510-530.
• (with Ulrich Stadtmüller). A pointwise limit theorems for counting processes of perturbed random walks, with an application to repeated significance tests. Sequential Anal. 36 (2017), 290-298.
• (with Anders Martin Löf). An asymmetric St. Petersburg game with trimming. Adv. Appl. Probab. 50A (2018), 115-129.
• (with Ulrich Stadtmüller). Variations of the elephant random walk. J. Appl. Probab. 58 (2021), 805-829.
• Oändligheten är inte som alla andra tal. Acta Acad. Reg. Sci. Upsaliensis 27 (2019), 65-83.
• (with Ulrich Stadtmüller). Elephant random walks with delays. Rev. Roumaine Math. Pures Appl. 67 (2022), 51-66.
• (with Ulrich Stadtmüller). The number of zeroes in Elephant random walks with delays. Statist. Probab. Lett. 174 (2021), 109112.
• (with Ulrich Stadtmüller). The elephant random walk with gradually increasing memory. Statist. Probab. Lett. 189 (2022), 109598.

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