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Publikationsliste Herr Prof. Dr. Peter Kern

Zur Veröffentlichung eingereicht:

  1. Barczy M. und Kern P.  (2024+): On Hölder continuity and pth-variation function of Weierstrass-type functions.
    https://arxiv.org/abs/2407.09229

In referierten Zeitschriften:

  1. Kern, P. und Scheffler, H.-P. (2025): Semistable distributions as marginals of operator stable laws. Statist. Probab. Letters 226, ariticle 110458.
    https://doi.org/10.1016/j.spl.2025.110458
  2. Kern, P. und Pleschberger, L. (2024): Parabolic fractal geometry of stable Lévy processes with drift. J. Fractal Geom., 11 no. 3/4 343–371
    https://doi.org/10.4171/jfg/152
  3. Kern, P. und Lage, S. (2023): On self-similar Bernstein functions and corresponding generalized fractional derivatives. J. Theoret. Probab., 36 348-371
    https://doi.org/10.1007/s10959-022-01166-0
  4. Kern, P. und Müller, C. (2022): A Closed Form Formula for the Stochastic Exponential of a Matrix-Valued Semimartingale. J. Stoch. Anal., 3(2) Article 3
    https://digitalcommons.lsu.edu/josa/vol3/iss2/3
  5. Kern, P. und Sönmez, E. (2019): On the carrying dimension of occupation measures for self-affine random fields. Probab. Math. Statist., 39(2) 459-479
    http://dx.doi.org/10.19195/0208-4147.39.2.12
  6. Kern, P., Lage, S. und Meerschaert, M. M. (2019): Semi-fractional diffusion equations. Fract. Calc. Appl. Anal., 22 326-357
    http://dx.doi.org/10.1515/fca-2019-0021
  7. Kern, P., Meerschaert, M. M. und Xiao, Y. (2018): Asymptotic behavior of semistable Lévy exponents and applications to fractal path properties. J. Theoret. Probab., 31 598-617
    http://dx.doi.org/10.1007/s10959-016-0720-6
  8. Kern, P. und Wedrich, L. (2017): On exact Hausdorff measure functions of operator semistable Lévy processes. Stoch. Anal. Appl., 35 980-1006
    http://dx.doi.org/10.1080/07362994.2017.1344556
  9. Bhatti, T. und Kern, P. (2017): An integral representation of dilatively stable processes with independent increments. Stochastic Process. Appl., 127 209-227
    http://dx.doi.org/10.1016/j.spa.2016.06.006
  10. Barczy, M. und Kern, P. (2016): A link between Bougerol's identity and a formula due to Donati-Martin, Matsumoto and Yor. Séminaire de Probabilités, 48 179-188
    http://dx.doi.org/10.1007/978-3-319-44465-9_6
  11. Kern, P. (2016): A general multiparameter version of Gnedenko's transfer theorem. Theory Probab. Appl., 60 134-142
    http://dx.doi.org/10.1137/S0040585X97T987569
  12. Barczy, M., Kern, P. und Pap, G. (2015): Dilatively stable stochastic processes and aggregate similarity. Aequat. Math., 89 1485-1507
    http://dx.doi.org/10.1007/s00010-014-0318-y
  13. Barczy, M., Kern, P. und Krause, V. (2015): Operator scaled Wiener bridges. ESAIM: Probab. Statist., 19 100-114
    http://dx.doi.org/10.1051/ps/2014016
  14. Kern, P. und Wedrich, L. (2015): Dilatively semistable stochastic processes. Statist. Probab. Letters, 99 101-108
    http://dx.doi.org/10.1016/j.spl.2015.01.008
  15. Finner, H., Kern, P. und Scheer, M. (2015): On some compound distributions with Borel summands. Insurance Math. Econom., 62 234-244
    http://dx.doi.org/10.1016/j.insmatheco.2015.03.012
  16. Kern, P. und Wedrich, L. (2014): Dimension results related to the St. Petersburg game. Probab. Math. Statist., 34 97-117
    http://www.math.uni.wroc.pl/~pms/files/34.1/Article/34.1.6.pdf
  17. Kern, P. und Wedrich, L. (2014): The Hausdorff dimension of operator semistable Lévy processes. J. Theoret. Probab., 27 383-403
    http://dx.doi.org/10.1007/s10959-012-0422-7
  18. Barczyk, A. und Kern, P. (2013): Scaling limits of coupled continuous time random walks and residual order statistics through marked point processes. Stochastic Process. Appl., 123 796-812
    http://dx.doi.org/10.1016/j.spa.2012.10.013
  19. Barczy, M. und Kern, P. (2013): Representations of multidimensional linear process bridges. Random Oper. Stoch. Equ., 21 159-189
    http://dx.doi.org/10.1515/rose-2013-0009
  20. Barczy, M. und Kern, P. (2013): Sample path deviations of the Wiener and the Ornstein-Uhlenbeck process from its bridges. Brazilian J. Probab. Statist., 27 437-466
    http://dx.doi.org/10.1214/11-BJPS175
  21. Jurlewicz, A., Kern, P., Meerschaert, M. M. und Scheffler, H.-P. (2012): Fractional governing equations for coupled random walks. Comp. Math. Appl., 64 3021-3036
    http://dx.doi.org/10.1016/j.camwa.2011.10.010
  22. Kern, P., Meerschaert, M. M. und Scheffler, H.-P. (2012): Correction: Limit theorems for coupled continuous time random walks. Ann. Probab., 40 890-891
    http://dx.doi.org/10.1214/10-AOP635
  23. Barczy, M. und Kern, P. (2011): General alpha-Wiener bridges. Commun. Stoch. Anal., 5 585-608
    https://www.math.lsu.edu/cosa/5-3-08[277].pdf
  24. Becker-Kern, P. und Pap, G. (2008): Parameter estimation of selfsimilarity exponents. J. Multivariate Anal., 99 117-140
    http://dx.doi.org/10.1016/j.jmva.2007.04.003
  25. Becker-Kern, P. (2007): Explicit representation of roots on p-adic solenoids and non-uniqueness of embeddability into rational one-parameter subgroups. Proc. Indian Acad. Sci. Math. Sci., 117 443-455
    http://dx.doi.org/10.1007/s12044-007-0037-6
  26. Becker-Kern, P. (2007): An almost sure limit theorem for mixtures of domains in random allocation. Studia Sci. Math. Hungar., 44 331-354
    http://dx.doi.org/10.1556/SScMath.2007.1024
  27. Becker-Kern, P. und Pap, G. (2007): A limit theorem for randomly stopped independent increment processes on separable metrizable groups. Math. Nachr., 280 1664-1680
    http://dx.doi.org/10.1002/mana.200510570
  28. Becker-Kern, P. (2007): Almost sure limit theorems of mantissa type for semistable domains of attraction. Acta Math. Hungar., 114 301-336
    http://dx.doi.org/10.1007/s10474-006-0532-8
  29. Becker-Kern, P. und Scheffler, H.-P. (2005): How to find stability in a purely semistable context. Yokohama Math. J., 51 75-88
    http://kamome.lib.ynu.ac.jp/dspace/bitstream/10131/5762/1/YMJ_51_N2_2005_075-088.pdf
  30. Becker-Kern, P. (2004): Existence of multivariate max-universal laws. Extremes, 7 377-391
    http://dx.doi.org/10.1007/s10687-004-3483-x
  31. Becker-Kern, P. (2004): Stochastic summability methods for domains of normal attraction of semistable laws. J. Math. Sci. (New York), 121 2603-2612
    http://dx.doi.org/10.1023/B:JOTH.0000027026.21519.45
  32. Becker-Kern, P. und Scheffler, H.-P. (2004): On multiple-particle continuous-time random walks. J. Appl. Math., 213-233
    http://dx.doi.org/10.1155/S1110757X04308065
  33. Becker-Kern, P. (2004): Random sums of independent random vectors attracted by (semi)-stable hemigroups. J. Appl. Anal., 10 83-104
    http://dx.doi.org/10.1515/JAA.2004.83
  34. Slavtchova-Bojkova, M., Becker-Kern, P. und Mitov, K. V. (2004): Total progeny in a subcritical branching process with two types of immigration. Pliska Stud. Math. Bulgar., 16 229-243
  35. Becker-Kern, P., Meerschaert, M. M. und Scheffler, H.-P. (2004): Limit theorem for continuous-time random walks with two time scales. J. Appl. Probab., 41 455-466
    http://www.jstor.org/stable/3216028
  36. Becker-Kern, P., Meerschaert, M. M. und Scheffler, H.-P. (2004): Limit theorems for coupled continuous time random walks. Ann. Probab., 32 730-756
    http://dx.doi.org/10.1214/aop/1079021462
  37. Becker-Kern, P. (2004): Random integral representation of operator-semi-self-similar processes with independent increments. Stochastic Process. Appl., 109 327-344
    http://dx.doi.org/10.1016/j.spa.2003.10.003
  38. Becker-Kern, P., Meerschaert, M. M. und Scheffler, H.-P. (2003): Hausdorff dimension of operator stable sample paths. Monatsh. Math., 140 91-101
    http://dx.doi.org/10.1007/s00605-002-0534-8
  39. Becker-Kern, P. (2003): Stable and semistable hemigroups: domains of attraction and self-decomposability. J. Theoret. Probab., 16 573-598
    http://dx.doi.org/10.1023/A:1025664314657
  40. Meerschaert, M. M., Benson, D. A., Scheffler, H.-P. und Becker-Kern, P. (2002): Governing equations and solutions of anomalous random walk limits. Phys. Rev. E, 66 4
    http://link.aps.org/doi/10.1103/PhysRevE.66.060102
  41. Becker-Kern, P. (2002): Limit theorems with random sample size for generalized domains of semistable attraction. J. Math. Sci. (New York), 111 3820-3829
    http://dx.doi.org/10.1023/A:1016522316478
  42. Becker-Kern, P. (2001): Max-semistable hemigroups: structure, domains of attraction and limit theorems with random sample size. Probab. Math. Statist., 21 441-465
    http://www.math.uni.wroc.pl/~pms/files/21.2/Article/21.2.12.pdf
  43. Scheffler, H.-P. und Becker-Kern, P. (2000): A law of the iterated logarithm for randomly stopped sums of heavy tailed random vectors. Monatsh. Math., 130 329-347
    http://dx.doi.org/10.1007/s006050070031.

Referierte Beiträge zu Tagungsbänden

  1. Kern, P. und Lage, S. (2021): Space-time duality for semi-fractional diffusions. U. Freiberg et al. (Eds.) Fractal Geometry and Stochastics VI. Progress in Probability 76, Birkhäuser, Basel, 255-272
    https://doi.org/10.1007/978-3-030-59649-1_11
  2. Becker-Kern, P. und Hazod, W. (2009): Mehler hemigroups and embedding of discrete skew convolution semigroups on simply connected nilpotent Lie groups. J. Hilgert et al. (Eds.), Infinite Dimensional Harmonic Analysis IV. World Sci. Publ., Hackensack, NJ, 32-46
    http://dx.doi.org/10.1142/9789812832825_0003

Unveröffentlichte Manuskripte

  1. Kern, P. , Neugebauer D., Rothe J., Schilling R. L., Stoyan D. und Weishaupt R. (2021): Cutting a Cake Is Not Always a "Piece of Cake": A Closer Look at the Foundations of Cake-Cutting Through the Lens of Measure Theory.
    https://arxiv.org/abs/2111.05402
  2. Barczy, M. und Kern, P. (2014): Gauss-Markov processes as space-time scaled stationary Ornstein-Uhlenbeck processes.
    http://arxiv.org/abs/1409.7253