List of publications of Prof. Dr. Peter Kern
Submitted for publication:
- Kern, P. and Pleschberger, L. (2024+): Parabolic Fractal Geometry of stable Lévy Processes with drift.
https://arxiv.org/pdf/2312.13800.pdf
Peer-reviewed journals:
- Kern, P. and Lage, S. (2023): On self-similar Bernstein functions and corresponding generalized fractional derivatives. J. Theoret. Probab., 36 (2023), 348-371
https://doi.org/10.1007/s10959-022-01166-0 - 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.
https://digitalcommons.lsu.edu/josa/vol3/iss2/3 - 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
http://dx.doi.org/10.19195/0208-4147.39.2.12 - Kern, P., Lage, S. and Meerschaert, M. M. (2019): Semi-fractional diffusion equations. Fract. Calc. Appl. Anal., 22 326-357
http://dx.doi.org/10.1515/fca-2019-0021 - 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
http://dx.doi.org/10.1007/s10959-016-0720-6 - Kern, P. and 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 - Bhatti, T. and 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 - 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
http://dx.doi.org/10.1007/978-3-319-44465-9_6 - 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 - Barczy, M., Kern, P. and 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 - Barczy, M., Kern, P. and Krause, V. (2015): Operator scaled Wiener bridges. ESAIM: Probab. Statist., 19 100-114
http://dx.doi.org/10.1051/ps/2014016 - Kern, P. and Wedrich, L. (2015): Dilatively semistable stochastic processes. Statist. Probab. Letters, 99 101-108
http://dx.doi.org/10.1016/j.spl.2015.01.008 - Finner, H., Kern, P. and 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 - Kern, P. and 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 - Kern, P. and 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 - 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
http://dx.doi.org/10.1016/j.spa.2012.10.013 - Barczy, M. and 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 - 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
http://dx.doi.org/10.1214/11-BJPS175 - 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
http://dx.doi.org/10.1016/j.camwa.2011.10.010 - Kern, P., Meerschaert, M. M. and 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 - Barczy, M. and Kern, P. (2011): General alpha-Wiener bridges. Commun. Stoch. Anal., 5 585-608
https://www.math.lsu.edu/cosa/5-3-08[277].pdf - Becker-Kern, P. and 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 - 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 - 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 - 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
http://dx.doi.org/10.1002/mana.200510570 - 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 - Becker-Kern, P. and 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 - Becker-Kern, P. (2004): Existence of multivariate max-universal laws. Extremes, 7 377-391
http://dx.doi.org/10.1007/s10687-004-3483-x - 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 - Becker-Kern, P. and Scheffler, H.-P. (2004): On multiple-particle continuous-time random walks. J. Appl. Math., 213-233
http://dx.doi.org/10.1155/S1110757X04308065 - 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 - 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
- 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
http://www.jstor.org/stable/3216028 - Becker-Kern, P., Meerschaert, M. M. and 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 - 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 - Becker-Kern, P., Meerschaert, M. M. and 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 - 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 - 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
http://link.aps.org/doi/10.1103/PhysRevE.66.060102 - 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 - 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 - 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
http://dx.doi.org/10.1007/s006050070031.
Peer-reviewed in proceedings:
- 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
https://doi.org/10.1007/978-3-030-59649-1_11 - 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
http://dx.doi.org/10.1142/9789812832825_0003
Unpublished manuscripts:
- 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.
https://arxiv.org/abs/2111.05402 - Barczy, M. and Kern, P. (2014): Gauss-Markov processes as space-time scaled stationary Ornstein-Uhlenbeck processes.
http://arxiv.org/abs/1409.7253