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2016 | OriginalPaper | Buchkapitel

6. Appendix

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Abstract

A positive measurable function , defined on some neighborhood of , is called slowly varying at if lim t →  ((ut)∕(t)) = 1 for all u > 0.

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Literatur
6.
Zurück zum Zitat G. Alsmeyer and A. Iksanov, A log-type moment result for perpetuities and its application to martingales in supercritical branching random walks. Electron. J. Probab. 14 (2009), 289–313.MathSciNetCrossRefMATH G. Alsmeyer and A. Iksanov, A log-type moment result for perpetuities and its application to martingales in supercritical branching random walks. Electron. J. Probab. 14 (2009), 289–313.MathSciNetCrossRefMATH
8.
Zurück zum Zitat G. Alsmeyer, A. Iksanov and M. Meiners, Power and exponential moments of the number of visits and related quantities for perturbed random walks. J. Theoret. Probab. 28 (2015), 1–40.MathSciNetCrossRefMATH G. Alsmeyer, A. Iksanov and M. Meiners, Power and exponential moments of the number of visits and related quantities for perturbed random walks. J. Theoret. Probab. 28 (2015), 1–40.MathSciNetCrossRefMATH
18.
Zurück zum Zitat S. Asmussen, Applied probability and queues. 2nd Edition, Springer-Verlag, 2003. S. Asmussen, Applied probability and queues. 2nd Edition, Springer-Verlag, 2003.
19.
Zurück zum Zitat K. B. Athreya, D. McDonald and P. Ney, Limit theorems for semi-Markov processes and renewal theory for Markov chains. Ann. Probab. 6 (1978), 788–797.MathSciNetCrossRefMATH K. B. Athreya, D. McDonald and P. Ney, Limit theorems for semi-Markov processes and renewal theory for Markov chains. Ann. Probab. 6 (1978), 788–797.MathSciNetCrossRefMATH
30.
Zurück zum Zitat Ju. K. Beljaev and V. M. Maksimov, Analytical properties of a generating function for the number of renewals. Theor. Probab. Appl. 8 (1963), 108–112.MathSciNet Ju. K. Beljaev and V. M. Maksimov, Analytical properties of a generating function for the number of renewals. Theor. Probab. Appl. 8 (1963), 108–112.MathSciNet
40.
Zurück zum Zitat P. Billingsley, Convergence of probability measures. Wiley, 1968.MATH P. Billingsley, Convergence of probability measures. Wiley, 1968.MATH
41.
Zurück zum Zitat P. Billingsley, Probability and measure. John Wiley & Sons, 1986.MATH P. Billingsley, Probability and measure. John Wiley & Sons, 1986.MATH
44.
Zurück zum Zitat N. H. Bingham, C. M. Goldie and J. L. Teugels, Regular variation. Cambridge University Press, 1989.MATH N. H. Bingham, C. M. Goldie and J. L. Teugels, Regular variation. Cambridge University Press, 1989.MATH
56.
65.
Zurück zum Zitat H. Carlsson and O. Nerman, An alternative proof of Lorden’s renewal inequality. Adv. Appl. Probab. 18 (1986), 1015–1016.MathSciNetMATH H. Carlsson and O. Nerman, An alternative proof of Lorden’s renewal inequality. Adv. Appl. Probab. 18 (1986), 1015–1016.MathSciNetMATH
68.
Zurück zum Zitat Y. S. Chow and H. Teicher, Probability theory: independence, interchangeability, martingales. Springer, 1988.CrossRefMATH Y. S. Chow and H. Teicher, Probability theory: independence, interchangeability, martingales. Springer, 1988.CrossRefMATH
69.
Zurück zum Zitat E. Çinlar, Introduction to stochastic processes. Prentice-Hall, 1975.MATH E. Çinlar, Introduction to stochastic processes. Prentice-Hall, 1975.MATH
71.
Zurück zum Zitat M. Csörgő, L. Horváth and J. Steinebach, Invariance principles for renewal processes. Ann. Probab. 15 (1987), 1441–1460.MathSciNetCrossRefMATH M. Csörgő, L. Horváth and J. Steinebach, Invariance principles for renewal processes. Ann. Probab. 15 (1987), 1441–1460.MathSciNetCrossRefMATH
81.
Zurück zum Zitat R. Durrett and T. Liggett, Fixed points of the smoothing transformation. Z. Wahrscheinlichkeitstheorie Verw. Geb. 64 (1983), 275–301.MathSciNetCrossRefMATH R. Durrett and T. Liggett, Fixed points of the smoothing transformation. Z. Wahrscheinlichkeitstheorie Verw. Geb. 64 (1983), 275–301.MathSciNetCrossRefMATH
88.
89.
Zurück zum Zitat W. Feller, An introduction to probability theory and its applications. Vol II, 2nd Edition. Wiley, 1971. W. Feller, An introduction to probability theory and its applications. Vol II, 2nd Edition. Wiley, 1971.
119.
Zurück zum Zitat A. Gut, Stopped random walks. Limit theorems and applications. 2nd Edition, Springer, 2009. A. Gut, Stopped random walks. Limit theorems and applications. 2nd Edition, Springer, 2009.
139.
Zurück zum Zitat A. Iksanov, On the number of empty boxes in the Bernoulli sieve I. Stochastics. 85 (2013), 946–959.MathSciNetMATH A. Iksanov, On the number of empty boxes in the Bernoulli sieve I. Stochastics. 85 (2013), 946–959.MathSciNetMATH
140.
Zurück zum Zitat A. Iksanov, Functional limit theorems for renewal shot noise processes with increasing response functions. Stoch. Proc. Appl. 123 (2013), 1987–2010.MathSciNetCrossRefMATH A. Iksanov, Functional limit theorems for renewal shot noise processes with increasing response functions. Stoch. Proc. Appl. 123 (2013), 1987–2010.MathSciNetCrossRefMATH
142.
Zurück zum Zitat A. Iksanov, Z. Kabluchko and A. Marynych, Weak convergence of renewal shot noise processes in the case of slowly varying normalization. Stat. Probab. Letters. 114 (2016), 67–77.MathSciNetCrossRefMATH A. Iksanov, Z. Kabluchko and A. Marynych, Weak convergence of renewal shot noise processes in the case of slowly varying normalization. Stat. Probab. Letters. 114 (2016), 67–77.MathSciNetCrossRefMATH
143.
Zurück zum Zitat A. Iksanov, Z. Kabluchko, A. Marynych and G. Shevchenko, Fractionally integrated inverse stable subordinators. Stoch. Proc. Appl., to appear (2017). A. Iksanov, Z. Kabluchko, A. Marynych and G. Shevchenko, Fractionally integrated inverse stable subordinators. Stoch. Proc. Appl., to appear (2017).
146.
Zurück zum Zitat A. Iksanov, A. Marynych and M. Meiners, Limit theorems for renewal shot noise processes with eventually decreasing response functions. Stoch. Proc. Appl. 124 (2014), 2132–2170.MathSciNetCrossRefMATH A. Iksanov, A. Marynych and M. Meiners, Limit theorems for renewal shot noise processes with eventually decreasing response functions. Stoch. Proc. Appl. 124 (2014), 2132–2170.MathSciNetCrossRefMATH
148.
Zurück zum Zitat A. Iksanov, A. Marynych and M. Meiners, Asymptotics of random processes with immigration I: Scaling limits. Bernoulli. 23, to appear (2017). A. Iksanov, A. Marynych and M. Meiners, Asymptotics of random processes with immigration I: Scaling limits. Bernoulli. 23, to appear (2017).
150.
Zurück zum Zitat A. M. Iksanov, A. V. Marynych and V. A. Vatutin, Weak convergence of finite-dimensional distributions of the number of empty boxes in the Bernoulli sieve. Theory Probab. Appl. 59 (2015), 87–113.MathSciNetCrossRefMATH A. M. Iksanov, A. V. Marynych and V. A. Vatutin, Weak convergence of finite-dimensional distributions of the number of empty boxes in the Bernoulli sieve. Theory Probab. Appl. 59 (2015), 87–113.MathSciNetCrossRefMATH
151.
Zurück zum Zitat A. Iksanov and M. Meiners, Exponential moments of first passage times and related quantities for random walks. Electron. Commun. Probab. 15 (2010), 365–375.MathSciNetCrossRefMATH A. Iksanov and M. Meiners, Exponential moments of first passage times and related quantities for random walks. Electron. Commun. Probab. 15 (2010), 365–375.MathSciNetCrossRefMATH
157.
Zurück zum Zitat A. Iksanov and S. Polotskiy, Tail behavior of suprema of perturbed random walks. Theory Stochastic Process. 21(36) (2016), 12–16.MATH A. Iksanov and S. Polotskiy, Tail behavior of suprema of perturbed random walks. Theory Stochastic Process. 21(36) (2016), 12–16.MATH
160.
Zurück zum Zitat J. Jacod and A. N. Shiryaev, Limit theorems for stochastic processes. 2nd Edition, Springer, 2003. J. Jacod and A. N. Shiryaev, Limit theorems for stochastic processes. 2nd Edition, Springer, 2003.
162.
Zurück zum Zitat S. Janson, Moments for first-passage and last-exit times, the minimum, and related quantities for random walks with positive drift. Adv. Appl. Probab. 18 (1986), 865–879.MathSciNetCrossRefMATH S. Janson, Moments for first-passage and last-exit times, the minimum, and related quantities for random walks with positive drift. Adv. Appl. Probab. 18 (1986), 865–879.MathSciNetCrossRefMATH
177.
Zurück zum Zitat H. Kesten and R. A. Maller, Two renewal theorems for general random walks tending to infinity. Probab. Theory Relat. Fields.106 (1996), 1–38.MathSciNetCrossRefMATH H. Kesten and R. A. Maller, Two renewal theorems for general random walks tending to infinity. Probab. Theory Relat. Fields.106 (1996), 1–38.MathSciNetCrossRefMATH
188.
Zurück zum Zitat T. G. Kurtz and P. Protter, Weak limit theorems for stochastic integrals and stochastic differential equations. Ann. Probab. 19 (1991), 1035–1070.MathSciNetCrossRefMATH T. G. Kurtz and P. Protter, Weak limit theorems for stochastic integrals and stochastic differential equations. Ann. Probab. 19 (1991), 1035–1070.MathSciNetCrossRefMATH
236.
Zurück zum Zitat S. I. Resnick, Adventures in stochastic processes. 3rd printing, Birkhäuser, 2002. S. I. Resnick, Adventures in stochastic processes. 3rd printing, Birkhäuser, 2002.
251.
261.
Zurück zum Zitat W. Whitt, Stochastic-process limits: an introduction to stochastic-process limits and their application to queues. Springer, 2002.MATH W. Whitt, Stochastic-process limits: an introduction to stochastic-process limits and their application to queues. Springer, 2002.MATH
264.
Zurück zum Zitat B. B. Winter, Joint simulation of backward and forward recurrence times in a renewal process. J. Appl. Probab. 26 (1989), 404–407.MathSciNetCrossRefMATH B. B. Winter, Joint simulation of backward and forward recurrence times in a renewal process. J. Appl. Probab. 26 (1989), 404–407.MathSciNetCrossRefMATH
Metadaten
Titel
Appendix
verfasst von
Alexander Iksanov
Copyright-Jahr
2016
DOI
https://doi.org/10.1007/978-3-319-49113-4_6