Habilitation
Beiträge zur Summationstheorie von Folgen unabhängiger
Zufallsgrößen im Falle eines stabilen Grenzgesetzes.
Promotionsschrift B, Technische Universität Dresden, Sektion Mathematik,
1987 (anerkannt als Habilitation 1991)
Promotion
Konvergenzaussagen und asymptotische Entwicklungen für die
Verteilungsfunktion einer Summe unabhängiger identisch verteilter
Zufallsgrößen
im Falle einer stabilen Grenzverteilungsfunktion.
Dissertationsschrift A, Technische Universität Dresden, Sektion
Mathematik, 1978.
Thesen: Wiss. Zeitschrift der Techn. Univ. Dresden, 28(1979), 1217-1218
1974 - 1979 |
1980 - 1989 |
1990 - 1999 |
2000 - 2009 |
ab 2010
ab 2010
- G. Christoph, V.V. Ulyanov and V.E. Bening (2019)
Second Order Expansions for Sample Median with
Random Sample Size
in: "arXiv:1905.07765v1".
- G. Christoph, M.M. Monakhov and V.V. Ulyanov (2017)
Second-order Chebyshev-Edgeworth and Cornish-Fisher expansions for distributions
of statistics constructed with respect
to samples of random size. (in Russian)
in: " Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI)", Vol. 466, Veroyatnost' i Statistika, Vol. 26, pp. 167 - 207.
see: https://www.researchgate.net/publication/324089834
English version see Preprint: http://www.math.sci.hiroshima-u.ac.jp/stat/TR/TR17/TR17-15.pdf
(DOI: 10.13140/RG.2.2.28836.17281)
- Gerd Christoph, Vladimir V. Ulyanov and Yasunori Fujikoshi (2013)
Accurate Approximation of Correlation Coefficients by Short Edgeworth-Chebyshev Expansion and Its Statistical Applications
in: Prokhorov and Contemporary Probability Theory : In Honor of Yuri V. Prokhorov / edited by Albert N. Shiryaev,
S. R. S. Varadhan, Ernst L. Presman, Springer Proceedings in Mathematics & Statistics ; 33, Springer, pp. 239-260, 2013
Online-Ressource ISBN 978-3-642-33549-5 , print 978-3-642-33548-8
- G. Christoph, Yu. Prohorov and V. Uljanov (2012)
Characterization and stability problems for finite quadratic
forms
in: Yu. V. Prohorov , Selected Works (in Russian), ed. Gamkrelidze, TORUS PRESS, Moscow, 654 - 666, 2012.
first published in
"Asymptotic Methods in Probability and
Statistics with Applications",
Balakrishnan (ed.) et al.,
Birkhäuser, Boston, 2001, pp. 39 - 50.
- Yu. Prohorov, G. Christoph and V. Uljanov (2012)
On characterizing properties of quadratic forms
in: Yu. V. Prohorov , Selected Works (in Russian), ed. Gamkrelidze, TORUS PRESS, Moscow, 649 - 653, 2012.
first published
in: Doklady Akademii Nauk / Rossijskaja Akademija
Nauk, vol. 373, no. 2, 2000, pp. 168 - 170 (in Russian)
English translation: Doklady Mathematics, Vol. 62, No. 1, 2000 pp. 39-41
- G. Christoph, Yu. Prohorov and V. Uljanov (2012)
On Distribution of Quadratic Forms in Gaussian Random Variables
in: Yu. V. Prohorov , Selected Works (in Russian), ed. Gamkrelidze, TORUS PRESS, Moscow, 560 - 574, 2012.
first published
in: Teor. Veroyatn. Primen. 40, Nr. 2 (1995), pp. 301 - 312.
English translation in: Theory Prob. Appl. 40, Nr. 2 (1995), pp.
250-260.
- G. Christoph and S. Malov (2012)
Asymptotic Properties of Generalized
Multivariate Rank Statistics.
in: "Communications in Statistics – Theory and Methods", Vol. 41, Nr. 12, pp. 2133 - 2159.
(DOI: 10.1080/03610926.2011.558662)
- G. Christoph and V. Ulyanov (2011)
On Accurate Approximation of Standardized Chi-Squared
Distributions by Edgeworth-Chebyshev Expansions.
in: "Informatics and Its Applications", Vol.5, Nr. 1, 25-31.
- G. Christoph, N. Malevich (2011)
Second Order Behavior of the Tails of Compound Sums of Regulary Varying Random Variables.
in: Mathematics in Engineering, Science and Aerospace” (MESA), Vol. 2, Nr. 3, pp. 235 - 242.
- Gerd Christoph (2011))
Dem Zufall auf der Spur -
Ein Blick in die Geschichte der Stochastik
in: "Historisches für den Unterricht nutzbar gemacht", Herausgeber H. Henning und F. Freise, Istron Band 17, S.56-65
Verlag Franzbecker
- G. Christoph and V. Ulyanov (2010)
On accuracy of approximation of standardized chi-squared distributions by the normal law,
in: "Proceedings of the International Symposium on Stochastic Models in Reliability Engeneering, Life Science and Operations Management",
Beer Sheva, Israel, February 8-11, 2010 , I. Frenkel (ed.) et al.,
Beer Sheva, 2010, pp. 150 - 154.
- G. Christoph und H. Hackel (2010)
Starthilfe Stochastik, ISBN 978-3-519-00341-0, Vieweg+Teubner, Nachdruck 2010 der Erstausgabe 2002, 120 Seiten
2000 - 2009
- Bräsel, Heidemarie; Christoph, Gerd; Grunau, Hans-Christoph; Henk, Martin; Henning, Herbert; Kahle, Waltraud;
Kaibel, Volker; Manteuffel, Karl; Pott, Alexander; Warnecke, Gerald; Willems, Wolfgang (2009)
"Alles was zählt!" - der mathematische Blick,
Technical Report / Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik; 2009.
- G. Christoph and S.V. Malov (2009)
On semiparametric estimation in copula models under right censored data
in: S.M. Ermakov (ed.) et al., "Simulation 2009, 6th St. Petersburg Workshop on Simulation", 2009.06.28-07.04
St. Petersburg : VVM com. Ltd., ISBN 978-5-9651035-4-6. - 2009, S. 335-340
- V. Ulyanov, G. Christoph and Y. Fujikoshi (2006)
On approximations of transformed chi-squared distributions in statistical applications<
in: "Siberian Mathematical Journal", Volume 47, Number 6, 2006, pp. 1154-1166.
Translated from "Sibirskii matematicheskii Zhurnal, Vol. 47, No. 6, pp. 1401-1413.
(see also: Preprint 2006-14 Berry-Esseen Type Bounds for Transformations of Chi-Squared Variables
and Its Statistical Applications
- G. Christoph, V. Ulyanov (2006)
Bounds for L_1-approximation of chi-squared-density by a first order Chebyshev-Edgeworth-expansion,
in: "Communications in Dependability and Quality Management: An International Journal", Volume 9, Number 1, 2006, pp. 12-16.
ISSN 1450-7196.
- G. Christoph (2005)
Exact rates of convergence to ruin probabilities for regularly varying claims
in: "Simulation 2005, Proceedings of the 5th St. Petersburg Workshop on Simulation",
St.Petersburg, Russia, June 26 - July 2, 2005 ,
S.M. Ermakov (ed.) et al.,
Saint Petersburg, University Publishers, 2005, pp. 209 - 214.
- G. Christoph (2005)
Exact rates of convergence to ruin probabilities for regularly varying random variables
in: "Proceedings of the International Symposium on Stochastic Models in Reliability, Safety, Security and Logistics",
Beer Sheva, Israel, February 15-17, 2005 ,
I. Frenkel (ed.) et al.,
Beer Sheva - Riga, 2005, pp. 75 - 78. ISBN 9984-668-79-7
- G. Christoph (2004)
Exact rates of convergence for compound sums of random variables with common regularly varying distribution functions
in: "Longevity, Aging and Degradation Models in Reliability, Public Health,
Medicine and Biology", Vol.2,
V. Antonov (ed.) et al.,
St. Petersburg, 2004, pp. 56 - 67. ISBN 5-7422-0638-0
(see also Preprint 2004-15)
- G. Christoph (2003)
Scaling by discrete self-decomposable random variables
in: "Kolmogorov and Contemporary Mathematics",
International Conference in Commemoration of the Centennial of Andrei Nikolaevich Kolmogorov, Moscow, June 16-21, 2003,
Yu. S. Osipov (ed.) et al.,
Moscow, 2003, pp. 412 - 413.
- G. Christoph (2003)
Limit Theorems of Probability Theory
in: Probability and Statistics,
edited by Reinhard Viertl, in vol.Encyclopedia of Mathematical Science
Encyclopedia of Life Support Systems (EOLSS) ,
Developed under the Auspices of the UNESCO, EOLSS Publishers, Oxford, UK, http://www.eolss.net/ , 27 pages
Registration for free trial for a period of 24 hours under:
https://www.eolss.org/EolssRegister/RegisterFreeUser.aspx
- G. Christoph (Mitautor, Herausgeber: F. Beichelt, D.C. Montgomery) (2003)
Teubner-Taschenbuch der Stochastik, ISBN 3-519-00457-7, Teubner, 2003, 466 Seiten
- G. Christoph und H. Hackel (2002)
Starthilfe Stochastik, ISBN 3-519-00341-4, Teubner, 2002, 120 Seiten
- G. Christoph (2002)
Asymptotic expansions with discrete stable limit laws
in: "Limit Theorems in Probability and Statistics", Vol.1,
I. Berkes (ed.) et al.,
Bolyai Mathematical Society, Hungary, 2002, pp. 293 - 303
(see also Preprint 99-21)
- G. Christoph and K. Schreiber (2001)
Positive Linnik and discrete Linnik distributions
in: "Asymptotic Methods in Probability and
Statistics with Applications",
Balakrishnan (ed.) et al.,
Birkhäuser, Boston, 2001, pp. 3 - 18.
(see also Preprint 99-17)
- G. Christoph, Yu. Prohorov and V. Uljanov (2001)
Characterization and stability problems for finite quadratic
forms
in: "Asymptotic Methods in Probability and
Statistics with Applications",
Balakrishnan (ed.) et al.,
Birkhäuser, Boston, 2001, pp. 39 - 50.
(see also Preprint 99-04)
- Yu. Prohorov, G. Christoph and V. Uljanov (2000)
On characterizing properties of quadratic forms
in: Doklady Akademii Nauk / Rossijskaja Akademija
Nauk, vol. 373, no. 2, 2000, pp. 168 - 170 (in Russian)
English translation: Doklady Mathematics, Vol. 62, No. 1, 2000 pp. 39-41
- G. Christoph and K. Schreiber (2000)
Scaled Sibuya distribution and discrete
self-decomposability
in: Statistics & Probability Letters, 48 (2000), pp. 181 - 187
(see also Preprint 98-24)
1990 - 1999
- G. Christoph and K. Schreiber (1999)
Rates of convergence to stable and discrete stable laws
in: Probability Theory and Mathematical Statistics
Proceedings of the 7th Vilnius Conference (1998),
Grigelionis, B. (ed) et al., VSP International Science
Publishers, pp. 147 - 156
(see also Preprint 98-36)
- A. Lehmann, H. Wendt und G. Christoph (1999)
Statistische Datenanalyse zur Elbwasserbeschaffenheit
Magdeburger Wissenschaftslournal 99/1, Otto-von-Guericke-Universität Magdeburg
- G. Christoph and K. Schreiber (1998)
The Generalized Discrete Linnik Distributions
Advances in Stochastic Models for Reliability,
Quality and Safety; editors: W. Kahle, E. v. Collani, J. Franz,
U. Jensen;
Birkhäuser Boston, 1998, pp. 3 - 18.
(see also Preprint 97-24)
- G. Christoph and K. Schreiber (1998)
Discrete Stable Random Variables
in: Statistics & Probability Letters 37 (1998), pp. 243 - 247.
(see also Preprint 97-05)
- G. Christoph and M. Falk (1996)
A Note on Domains of p-max Stable Laws
in: Statistics & Probability Letters 28 (1996), pp. 279 - 284.
(see also Preprint 94-14)
- G. Christoph, Yu. Prohorov and V. Uljanov (1995)
On Distribution of Quadratic Forms in Gaussian Random Variables
in: Teor. Veroyatn. Primen. 40, Nr. 2 (1995), pp. 301 - 312.
English translation in: Theory Prob. Appl. 40, Nr. 2 (1995), pp.
250-260.
(see also Preprint 95-07)
- G. Christoph and W. Wolf (1993)
Convergence Theorems with a Stable Limit Law.
Akademie Verlag, Reihe Mathematical Research, 1993, 200 pages.
- G. Christoph (Mitautor, Herausgeber: P. H. Müller) (1991):
Lexikon der Stochastik
5. überarbeitete Auflage, Akademie-Verlag, 1991.
- G. Christoph (1991)
Non-uniform Estimates in Limit Theorems with a Stable Limit
Distribution
Math. Nachrichten 153 (1991), pp. 257 - 272.
- G. Christoph (1991)
On Some Differences in Limit Theorems with a Normal and a
Non-normal Stable Limit Law
Math. Nachrichten 153 (1991), pp. 247 - 256.
1980 - 1989
- G. Christoph (1987)
A Series Criterion for the Convergence Rate to a Stable Law
in: Limit Theorems in Probability Theory and Related Fields, Techn.
Univ. Dresden. Serie: Wissenschaft, Theorie und Praxis (1987),
pp. 59 - 67.
- G. Christoph (1987)
Strong Approximation of Partial Sums of i.i.d. Random Variables
Attracted to a Stable Law
Math. Nachrichten 134 (1987), pp. 277 - 282.
- G. Christoph (1987)
Non-uniform Estimates of the Remainder Term in Limit Theorems with
a Stable Limit Law
in: Proceedings of IV. International Vilnius Conference on
Probability Theory and Mathematical Statistics, 1985, vol. 1,
VNU Science Press BV, Utrecht, 1987, pp. 357 - 362.
- G. Christoph (1986)
Weighted Sums of Random Variables Attracted to Stable Laws
Probab. Theory Rel. Fields 71 (1986), pp. 335 - 340.
- G. Christoph (1985)
Zur Berechnung der Pseudomomente von Zufallsgrößen
Wiss. Zeitschrift der Techn. Univ. Dresden 34 (1985), pp. 78 - 79.
- G. Christoph (1985)
Asymptotic Expansions of Distribution Functions of Sums of Random
Variables and of Sums of Reciprocals
of Random Variables in the Case
of Attraction to a Stable Law
Math. Nachrichten 122 (1985), pp. 91 - 98.
- G. Christoph (1984)
Asymptotic Expansions in Limit Theorems for Lattice Distributions
Attracted to Stable Laws
Math. Nachrichten 116 (1984), pp. 53 - 59.
- G. Christoph (1982)
Asymptotische Entwicklungen im Falle eines stabilen Grenzgesetzes II
(in Russisch)
Litovsk. Matem. Sb. 22 (1982) Nr. 1, pp. 69 - 79.
- G. Christoph (1981)
Asymptotische Entwicklungen im Falle eines stabilen Grenzgesetzes I
(in Russisch)
Litovsk. Matem. Sb. 21 (1981) Nr. 1, pp. 87 - 100, engl.
Übersetzung in: Liet. Matem. Rink. 21 (1981),
pp. 137 - 145.
- G. Christoph (1980)
Über notwendige und hinreichende Bedingungen für
Konvergenzaussagen im Falle einer stabilen Grenzverteilung
Zeitschr. Wahrscheinlichkeitstheorie verw. Gebiete 54 (1980) Nr. 1,
pp. 29 - 40.
1974 - 1979
- G. Christoph (1979)
Zur Konvergenzgeschwindigkeit im integralen Grenzwertsatz im Falle
einer stabilen Grenzverteilung (in Russisch)
Litovsk. Matem. Sb. 19 (1979) Nr. 1, pp. 129 - 141, engl.
Übersetzung in: Liet. Matem. Rink. 19 (1979) Nr. 1,
pp. 91 - 101.
- G. Christoph (1979)
Über die Konvergenzgeschwindigkeit im Falle einer stabilen
Grenzverteilung
Math. Nachrichten 90 (1979), pp. 21 - 30.
- G. Christoph (1974)
Asymptotische Entwicklungen für Dichtefunktionen von Summen
unabhängiger Zufallsgrößen
Wiss. Zeitschrift der Techn. Univ. Dresden 24 (1974) Nr. 3/4, pp.
539 - 548.
- G. Christoph (1974)
On Asymptotic Expansions for Densities of Independent Random
Variables (in Russisch)
Vestnik Leningrad. Univer. 7 (1974) Nr. 2, pp. 30 - 32.