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List of publications of Prof. Dr. Peter Kern

Submitted for publication:

  1. Kern, P. , Neugebauer D., Rothe J., Schilling R. L., Stoyan D. and 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.
    URL: https://arxiv.org/abs/2111.05402

Peer-reviewed journals:

  1. Kern, P. and Müller, C. (2022): A Closed Form Formula for the Stochastic Exponential of a Matrix-Valued Semimartingale. J. Stoch. Anal., 3(2), Article 3.
    URL: https://digitalcommons.lsu.edu/josa/vol3/iss2/3
  2. Kern, P. and Lage, S. (2022+): On self-similar Bernstein functions and corresponding generalized fractional derivatives. To appear in: J. Theoret. Probab.
    URL: https://doi.org/10.1007/s10959-022-01166-0
  3. Kern, P. and Sönmez, E. (2019): On the carrying dimension of occupation measures for self-affine random fields. Probab. Math. Statist., 39(2), 459-479
    URL: http://dx.doi.org/10.19195/0208-4147.39.2.12
  4. Kern, P., Lage, S. and Meerschaert, M. M. (2019): Semi-fractional diffusion equations. Fract. Calc. Appl. Anal., 22 326-357
    URL: http://dx.doi.org/10.1515/fca-2019-0021
  5. Kern, P., Meerschaert, M. M. and Xiao, Y. (2018): Asymptotic behavior of semistable Lévy exponents and applications to fractal path properties. J. Theoret. Probab., 31 598-617
    URL: http://dx.doi.org/10.1007/s10959-016-0720-6
  6. Kern, P. and Wedrich, L. (2017): On exact Hausdorff measure functions of operator semistable Lévy processes. Stoch. Anal. Appl., 35 980-1006
    URL: http://dx.doi.org/10.1080/07362994.2017.1344556
  7. Bhatti, T. and Kern, P. (2017): An integral representation of dilatively stable processes with independent increments. Stochastic Process. Appl., 127 209-227
    URL: http://dx.doi.org/10.1016/j.spa.2016.06.006
  8. Barczy, M. and 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
    URL: http://dx.doi.org/10.1007/978-3-319-44465-9_6
  9. Kern, P. (2016): A general multiparameter version of Gnedenko's transfer theorem. Theory Probab. Appl., 60 134-142
    URL: http://dx.doi.org/10.1137/S0040585X97T987569
  10. Barczy, M., Kern, P. and Pap, G. (2015): Dilatively stable stochastic processes and aggregate similarity. Aequat. Math., 89 1485-1507
    URL: http://dx.doi.org/10.1007/s00010-014-0318-y
  11. Barczy, M., Kern, P. and Krause, V. (2015): Operator scaled Wiener bridges. ESAIM: Probab. Statist., 19 100-114
    URL: http://dx.doi.org/10.1051/ps/2014016
  12. Kern, P. and Wedrich, L. (2015): Dilatively semistable stochastic processes. Statist. Probab. Letters, 99 101-108
    URL: http://dx.doi.org/10.1016/j.spl.2015.01.008
  13. Finner, H., Kern, P. and Scheer, M. (2015): On some compound distributions with Borel summands. Insurance Math. Econom., 62 234-244
    URL: http://dx.doi.org/10.1016/j.insmatheco.2015.03.012
  14. Kern, P. and Wedrich, L. (2014): Dimension results related to the St. Petersburg game. Probab. Math. Statist., 34 97-117
    URL: http://www.math.uni.wroc.pl/~pms/files/34.1/Article/34.1.6.pdf
  15. Kern, P. and Wedrich, L. (2014): The Hausdorff dimension of operator semistable Lévy processes. J. Theoret. Probab., 27 383-403
    URL: http://dx.doi.org/10.1007/s10959-012-0422-7
  16. Barczyk, A. and 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
    URL: http://dx.doi.org/10.1016/j.spa.2012.10.013
  17. Barczy, M. and Kern, P. (2013): Representations of multidimensional linear process bridges. Random Oper. Stoch. Equ., 21 159-189
    URL: http://dx.doi.org/10.1515/rose-2013-0009
  18. Barczy, M. and Kern, P. (2013): Sample path deviations of the Wiener and the Ornstein-Uhlenbeck process from its bridges. Brazilian J. Probab. Statist., 27 437-466
    URL: http://dx.doi.org/10.1214/11-BJPS175
  19. Jurlewicz, A., Kern, P., Meerschaert, M. M. and Scheffler, H.-P. (2012): Fractional governing equations for coupled random walks. Comp. Math. Appl., 64 3021-3036
    URL: http://dx.doi.org/10.1016/j.camwa.2011.10.010
  20. Kern, P., Meerschaert, M. M. and Scheffler, H.-P. (2012): Correction: Limit theorems for coupled continuous time random walks. Ann. Probab., 40 890-891
    URL: http://dx.doi.org/10.1214/10-AOP635
  21. Barczy, M. and Kern, P. (2011): General alpha-Wiener bridges. Commun. Stoch. Anal., 5 585-608
    URL: https://www.math.lsu.edu/cosa/5-3-08[277].pdf
  22. Becker-Kern, P. and Pap, G. (2008): Parameter estimation of selfsimilarity exponents. J. Multivariate Anal., 99 117-140
    URL: http://dx.doi.org/10.1016/j.jmva.2007.04.003
  23. 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
    URL: http://dx.doi.org/10.1007/s12044-007-0037-6
  24. Becker-Kern, P. (2007): An almost sure limit theorem for mixtures of domains in random allocation. Studia Sci. Math. Hungar., 44 331-354
    URL: http://dx.doi.org/10.1556/SScMath.2007.1024
  25. Becker-Kern, P. and Pap, G. (2007): A limit theorem for randomly stopped independent increment processes on separable metrizable groups. Math. Nachr., 280 1664-1680
    URL: http://dx.doi.org/10.1002/mana.200510570
  26. Becker-Kern, P. (2007): Almost sure limit theorems of mantissa type for semistable domains of attraction. Acta Math. Hungar., 114 301-336
    URL: http://dx.doi.org/10.1007/s10474-006-0532-8
  27. Becker-Kern, P. and Scheffler, H.-P. (2005): How to find stability in a purely semistable context. Yokohama Math. J., 51 75-88
    URL: http://kamome.lib.ynu.ac.jp/dspace/bitstream/10131/5762/1/YMJ_51_N2_2005_075-088.pdf
  28. Becker-Kern, P. (2004): Existence of multivariate max-universal laws. Extremes, 7 377-391
    URL: http://dx.doi.org/10.1007/s10687-004-3483-x
  29. Becker-Kern, P. (2004): Stochastic summability methods for domains of normal attraction of semistable laws. J. Math. Sci. (New York), 121 2603-2612
    URL: http://dx.doi.org/10.1023/B:JOTH.0000027026.21519.45
  30. Becker-Kern, P. and Scheffler, H.-P. (2004): On multiple-particle continuous-time random walks. J. Appl. Math., 213-233
    URL: http://dx.doi.org/10.1155/S1110757X04308065
  31. Becker-Kern, P. (2004): Random sums of independent random vectors attracted by (semi)-stable hemigroups. J. Appl. Anal., 10 83-104
    URL: http://dx.doi.org/10.1515/JAA.2004.83
  32. Slavtchova-Bojkova, M., Becker-Kern, P. and Mitov, K. V. (2004): Total progeny in a subcritical branching process with two types of immigration. Pliska Stud. Math. Bulgar., 16 229-243
  33. Becker-Kern, P., Meerschaert, M. M. and Scheffler, H.-P. (2004): Limit theorem for continuous-time random walks with two time scales. J. Appl. Probab., 41 455-466
    URL: http://www.jstor.org/stable/3216028
  34. Becker-Kern, P., Meerschaert, M. M. and Scheffler, H.-P. (2004): Limit theorems for coupled continuous time random walks. Ann. Probab., 32 730-756
    URL: http://dx.doi.org/10.1214/aop/1079021462
  35. Becker-Kern, P. (2004): Random integral representation of operator-semi-self-similar processes with independent increments. Stochastic Process. Appl., 109 327-344
    URL: http://dx.doi.org/10.1016/j.spa.2003.10.003
  36. Becker-Kern, P., Meerschaert, M. M. and Scheffler, H.-P. (2003): Hausdorff dimension of operator stable sample paths. Monatsh. Math., 140 91-101
    URL: http://dx.doi.org/10.1007/s00605-002-0534-8
  37. Becker-Kern, P. (2003): Stable and semistable hemigroups: domains of attraction and self-decomposability. J. Theoret. Probab., 16 573-598
    URL: http://dx.doi.org/10.1023/A:1025664314657
  38. Meerschaert, M. M., Benson, D. A., Scheffler, H.-P. and Becker-Kern, P. (2002): Governing equations and solutions of anomalous random walk limits. Phys. Rev. E, 66 4
    URL: http://link.aps.org/doi/10.1103/PhysRevE.66.060102
  39. Becker-Kern, P. (2002): Limit theorems with random sample size for generalized domains of semistable attraction. J. Math. Sci. (New York), 111 3820-3829
    URL: http://dx.doi.org/10.1023/A:1016522316478
  40. Becker-Kern, P. (2001): Max-semistable hemigroups: structure, domains of attraction and limit theorems with random sample size. Probab. Math. Statist., 21 441-465
    URL: http://www.math.uni.wroc.pl/~pms/files/21.2/Article/21.2.12.pdf
  41. Scheffler, H.-P. and Becker-Kern, P. (2000): A law of the iterated logarithm for randomly stopped sums of heavy tailed random vectors. Monatsh. Math., 130 329-347
    URL: http://dx.doi.org/10.1007/s006050070031.

  Peer-reviewed in proceedings:

  1. Kern, P. and 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
    URL: https://doi.org/10.1007/978-3-030-59649-1_11
  2. Becker-Kern, P. and 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
    URL: http://dx.doi.org/10.1142/9789812832825_0003

Unpublished manuscripts:

  1. Barczy, M. and Kern, P. (2014+): Gauss-Markov processes as space-time scaled stationary Ornstein-Uhlenbeck processes.
    URL: http://arxiv.org/abs/1409.7253
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