Professur fr Wahrscheinlichkeitstheorie

Verffentlichungen/ Papers & Preprints


  1. (mit / with Yuri Kondratiev and Yuliia Mishura) Asymptotic behaviour and functional limit theorems for a time changed Wiener process.
    [pdf]  [arXiv] [journal] DOI:
  2. (mit / with Victoria Knopova) Bochner's Subordination and Fractional Caloric Smoothing in Besov and Triebel-Lizorkin Spaces (submitted)
    [pdf]  [arXiv] [journal] DOI:
  3. (mit / with Dietrich Stoyan) Continuity Assumptions in Cake-Cutting (submitted)
    [pdf]  [arXiv] [journal] DOI:


  1. (mit / with Toshihiro Uemura) Homogenization of symmetric Lvy processes on Rd.
    To appear: Revue Roumaine de Mathmatiques Pures et Appliques
    [pdf]  [arXiv] [journal] DOI:
  2. (mit / with Kamil Kaleta) Progressive intrinsic ultracontractivity and heat kernel estimates for non-local Schrdinger operators.
    Journal of Functional Analysis 279 (2020) 108606 (69 pp)
    [pdf]  [arXiv] []
  3. (mit / with Georg Berschneider) Die Poisson-Verteilung, Fuballtore und das Gesetz der kleinen Zahlen
    To appear: Der Mathematikunterricht 65 Heft 6 (2019) 40-53
    [pdf]  [arXiv] [journal] DOI:
  4. (mit / with Mingjie Liang and Jian Wang) A unified approach to coupling SDEs driven by Lvy noise and some applications.
    Bernoulli 26 (2020) 664-693
    [pdf]  [arXiv] []
  5. (mit / with Changsong Deng) Exact Asymptotic Formulas for the Heat Kernels of Space and Time-Fractional Equations.
    Fractional Calculus and Applications 22 (2019) 968-989
    [pdf]  [arXiv] []
  6. (mit / with Bjrn Bttcher and Martin Keller-Ressel)  Distance multivariance: new dependence measures for random vectors. (plus 9 pp. online supplement)
    The Annals of Statistics 47 (2019) 2757-2789
    [pdf]  [arXiv] [] [Supplement]
  7. (mit / with Franziska Khn) Strong convergence of the Euler-Maruyama approximation for a class of Lvy-driven SDEs.
    Stochastic Processes and their Applications 129 (2019) 2654-2680.
    [pdf]  [correction of misprints]  [arXiv] []
  8. (mit / with Franziska Khn) A probabilistic proof of Schoenberg's theorem.
    Journal of Mathematical Analysis and Applications 476 (2019) 13-26
    [pdf]  [arXiv] []
  9. (mit / with Franziska Khn) On the domain of fractional Laplacians and related generators of Feller processes.
    Journal of Functional Analysis 276 (2019) 2397-2439
    [pdf]  [arXiv]   [] 
  10. (mit / with Ante Mimica & Nikola Sandric)  Markov chain approximation of pure jump processes.
    Acta Applicandae Mathematica 158 (2018) 167-206
    [pdf]  [arXiv] []
  11. (mit / with Bjrn Bttcher and Martin Keller-Ressel)  Detecting independence of random vectors: generalized distance covariance and Gaussian covariance. Modern Stochastics: Theory and Applications 5 (2018) 353-383
      [arXiv] []
  12. (mit / with Victoria Knopova) A Probabilistic proof of the breakdown of Besov regularity in L-shaped domains.
    In: Eberle, A. et al: Stochastic Partial Differential Equations and Related Fields (Conference Proceedings in Honor of Michael Rckner, Bielefeld, Germany, October 10-14 2016). Springer, Proceedings in Mathematics & Statistics 229, Cham 2018, pp. 473-488..
     [pdf]  [arXiv] []
  13. (mit / with Chang-Song Deng) Harnack inequalities for SDEs driven by time-changed Brownian motions.
    Electronic Journal of Probability 22 (2017) no. 71 pp. 1-23
    [pdf]  [arXiv] []
  14. (mit / with Chang-Song Deng and Yan-Hong Song) Sub-geometric rates of convergence for Markov processes under subordination
    Advances in Applied Probability 49 (2017) 162-181.
    [pdf]  [arXiv] []
  15. (mit/with Zoran Vondracek) Absolute continuity and singularity of probability measures induced by a purely discontinuous Girsanov transform of a stable process.
    Trans. Am. Math. Soc. 369 (2017) 1547-1577
    [pdf]  [arXiv] []
  16. (mit / with Chang-Song Deng) Complete Bernstein functions and subordinators with nested ranges. A note on a paper by P. Marchal..
    Electronic Communications in Probability 21 (2016) paper 78, pp. 1-5
    [pdf]  [arXiv]  []
  17. (mit/with Franziska Khn) Moderate deviations and Strassen's law for additive processes. 
    J. Theor. Probab.
    29 (2016) 632-652.
    [pdf]  [arXiv] []
  18. (mit/with Boris Baeumer, Mihly Kovcs, Mark M. Meerschaert, Peter Straka) Reflected stable processes and their governing equations 
    Transactions of the American Mathematical Society
    368 (2016) 227-248
    [pdf]   [arXiv] []
  19. (mit/with Victoria Knopova) On level and collision sets of some Feller processes
    ALEA Latin American Journal of Probability and Mathematical Statistics 12 (2015) 1001-1029.
    [pdf]  [arXiv] [journal] DOI:
  20. (mit / with Mihly Kovcs and Felix Lindner) Weak convergence of finite element approximations of linear stochastic evolution equations with Lvy noise.
    SIAM/ASA Journal on Uncertainty Quantification 3 (2015) 1159-1199
    [pdf]  [arXiv]  []
  21. (mit/with Chang-Song Deng) On a Cameron-Martin type quasi-invariance theorem and applications to subordinate Brownian motion.
    Stochastic Analysis and Applications 33 (2015) 975-993.
    [pdf]  [arXiv]  [] 
  22. (mit/with Marcin Magdziarz) Asymptotic properties of Brownian motion delayed by inverse subordinators. 
    Proceedings of the American Mathematical Society 143 (2015) 4485-4501
    [pdf]  [arXiv] []
  23. (mit/with Chang-Song Deng) On shift Harnack inequalities for subordinate semigroups and moment estimates for Lvy processes.
    Stochastic Processes and their Applications 125 (2015) 3851-3878
    [pdf]  [arXiv] []
  24. (mit/with Victoriya Knopova, Jian Wang) Lower bounds of the Hausdorff dimension for the images of Feller processes. 
    Statistics and Probability Letters 97 (2015) 222-228
    [pdf]  [arXiv] []
  25. Martingales. In: James D. Wright (editor-in-chief): International Encyclopedia of the Social & Behavioral Sciences (2nd ed), Vol 14. Oxford: Elsevier. pp. 630634.
    [pdf]    [preprint]    []
  26. (mit/with Jian Wang) Lower bounded semi-Dirichlet forms associated with Lvy type operators. In: Z-Q. Chen, N. Jacob, M. Takeda, T. Uemura: Festschrift Masatoshi Fukushima. In Honor of Masatoshi Fukushima's Sanju. World Scientific, New Jersey 2015, pp. 507-527.
    [pdf]   [arXiv] []
  27. (mit/with Mark Meerschaert, Alla Sikorskii) Stochastic solutions for fractional wave equations.
    Nonlinear Dynamics
    80 (2015) 1685-1695.
    [pdf]  [arXiv] []
  28. (mit/with Nikolai Leonenko, Mark Meerschaert, Alla Sikorskii) Correlation structure of time-changed Lvy processes. 
    Communications in Applied and Industrial Mathematics
    6 (2014), p. e-483 (22 pp.).
    [pdf]  [arXiv] []
  29. (mit/with Gilles Guillot, Emilio Porcu, Moreno Bevilacqua) Validity of covariance models for the analysis of geographical variation. Methods in Ecology and Evolution 5 (2014) 329-335.
    [pdf]   [arXiv] []
  30. (mit/with P.A. Cioica, S. Dahlke, N. Dhring, U. Friedrich, S. Kinzel, F. Lindner, T. Raasch, K. Ritter) On the convergence analysis of spatially adaptive Rothe methods. Foundations of Computational Mathematics 14 (2014) 863-912.
    [pdf] [arXiv] []
  31. (mit/with Victorya Knopova) On the small-time behaviour of Lvy-type processes. Stochastic Processes and their Applications 124 (2014) 2249-2265
    [pdf]   [arXiv] []
  32. (mit/with Mikhail Lifshits, Ilya Tyurin) A probabilistic inequality related to negative definite functions. 
    In: C. Houdre et al. (eds.): High Dimensional Probability VI. The Banff Volume. Birkhuser, Progress in Probability 66, Basel 2013, pp. 73-80.
    [pdf] [arXiv] []
  33. (mit/with Jian Wang) Some theorems on Feller processes: transience, local times and ultracontractivity.
    Trans. Am. Math. Soc. 365 (2013) 3255-3286.
    [pdf] [arXiv] []
  34. (mit/with Felix Lindner) Weak order for the discretization of the stochastic heat equation driven by impulsive noise.
    Potential Analysis 38 (2013) 345-379.
    [pdf] [arXiv] []
  35. (mit/with Victorya Knopova) A note on the existence of transition probability densities for Lvy processes.
    Forum Math. 25 (2013) 125-149.
    [pdf] [arXiv] []
  36. (mit/with Krzysztof Burdzy & Tadeusz Kulczycki) Stationary distributions for jump processes with inert drift.
    In: J. Feng, Y. Hu, E. Nualart and V. Viens (eds.): Malliavin Calculus and Stochastic Analysis. A Festschrift in Honour of David Nualart . Springer Proceedings in Mathematics and Statistics 34, Springer, New York 2013, pp. 139-172.
    [pdf] [arXiv] []
  37. (mit/with Yana A. Butko, Oleg G. Smolyanov) Lagrangian and Hamiltonian Feynman Formulae for some Feller Semigroups and Their Perturbations.
    Infinite Dimensional Analysis, Quantum Probability and Related Topics 15 (2012) 1250015 (26 pages)
    [pdf] [arXiv] []
  38. (mit/with Jian Wang) Functional inequalities and subordination: stability of Nash and Poincar inequalities.
    Math. Z. 272 (2012) 921-936
    [pdf] [arXiv] []
  39. (mit/with Pawel Sztonyk, Jian Wang) Coupling property and gradient estimates for Lvy processes via the symbol.
    Bernoulli 18 (2012) 1128-1149
    [pdf] [arXiv] []
  40. (mit/with Jian Wang) Strong Feller continuity of Feller processes and semigroups.
    Infinite Dimensional Analysis, Quantum Probability and Related Topics 15 (2012) 1250010-1 - 1250010-28
    [pdf] [arXiv] []
  41. (mit/with Davar Khoshnevisan, Yimin Xiao) Packing Dimension Profiles and Lvy Processes.
    Bull. London Math. Soc. 44 (2012), 931-942.
    [pdf] [arXiv] []
  42. (mit/with John Oberdick, Karl Schilling) Towards an efficient and integrative analysis of limited-choice behavioral experiments.
    The Journal of Neuroscience 32 (2012), 12651-12656. (Toolbox paper)
    [pdf] [arXiv] []
  43. (mit/with P. Cioica, S. Dahlke, N. Dhring, S. Kinzel, F. Lindner, T. Raasch, K. Ritter) Adaptive Wavelet Methods for the stochastic Poisson Equation. BIT Numer. Math. 52 (2012), 589-614
    [pdf] []
  44. (mit/with Krzysztof Burdzy & Tadeusz Kulczycki) Stationary distributions for jump processes with memory.
    Ann. Inst. Henri Poincar: Probab. & Stat. 48 (2012) 609-630.
    [pdf] [arXiv] []
  45. (mit/with Niels Jacob, Victorya Knopova, Sandra Landwehr) A geometric interpretation of the transition density of a symmetric Lvy process.
    Science China: Mathematics 55 (2012), 1099-1126.
    [pdf] [arXiv] []
  46. (mit/with Jian Wang) On the coupling property and the Liouville theorem for Ornstein-Uhlenbeck processes.
    J. Evol. Equ. 12 (2012) 119-140.
    [pdf] [arXiv] []
  47. (mit/with Victorya Knopova) Transition density estimates for a class of Lvy and Lvy-type processes.
    J. Theor. Probab. 25 (2012) 144-170.
    [pdf] (with corrections) [arXiv] []
  48. (mit/with Toshihiro Uemura) On the structure of the domain of a symmetric jump type Dirichlet form.
    Publ. RIMS Kyoto Univ. 40 (2012), 1-20.
    [pdf] [arXiv] []
  49. (mit/with P. Cioica, S. Dahlke, S. Kinzel, F. Lindner, T. Raasch, K. Ritter) Spatial Besov Regularity for Stochastic Partial Differential Equations on Lipschitz domains.
    Studia Math. 207 (2011) 197-234.
    [pdf] [arXiv] []
  50. (mit/with Bjrn Bttcher, Yana A. Butko & Oleg G. Smolyanov) Feynman formulas and path integrals for some evolution equations related to \tau-quantization.
    Russ. J. Math. Phys .18 (2011) 387-399.
    [pdf] [arXiv] []
  51. (mit/with Sebastian Harth, Elke R. Gizewski, Martin Obert, Christina Schulte-Gers & Marcel A. Verhoff) Age and gender dependent bone density changes of the human skull disclosed by high-resolution flat-panel computed technology.
    Intnl. J. Legal Medicine 125 (2011) 417-425.
    [pdf] [arXiv] []
  52. (mit/with Jian Wang) On the coupling property of Lvy processes.
    Ann. Inst. Henri Poincar: Probab & Stat 47 (2011), 1147-1159.
    [pdf] [arXiv] []
  53. (mit/with Yana A. Butko & Oleg G. Smolyanov) Hamiltonian Feynman-Kac and Feynman formulae for dynamics of particles with position-dependent mass.
    Int. J. Theor. Physics 50 (2011), 2009-2018.
    [pdf] [arXiv] []
  54. (mit/with Bjrn Bttcher & Jian Wang) Constructions of Coupling Processes for Lvy Processes and Their Applications.
    Stochastic Processes and their Applications 121 (2011) 1201-1216
    [pdf] [arXiv] []
  55. (mit/with Emilio Porcu) From Schoenberg to Pick-Nevanlinna: towards a complete picture of the variogram class.
    Bernoulli 17 (2011) 441-455
    [pdf] [arXiv] []
  56. (mit/with Alexander Schnurr) The symbol associated with the solution of a stochastic differential equation.
    El. J. Probab. 15 (2010) 1369-1393
    [pdf] [arXiv] []
  57. (mit/with Ya. A. Butko & O.G. Smolyanov) Feynman Formulae for Feller Semigroups.
    Doklady Mathematics 82 (2010) 679-683.
    [pdf] [arXiv] []
    Russian Original: Formuly Feynmana dlya Fellerovskich Polugrupp
    Dokladi Adademii Nauk 434 (2010) 1-5.
    [pdf] [arXiv] [journal]
  58. (mit/with Sebastian Harth, Monika Klver, Martin Obert, Frank Ramsthaler, Christina Schulte-Geers, Horst Traupe & Marcel Veerhoff) High-resolution flat-panel volumetric CT images show no correlation between human age and suture obliteration - independent of sex.
    Forensic Science International 200 (2010) 180.e1-180e.12.
    [pdf] [arXiv] []
  59. (mit/with Guido Germano, Mauro Politi & Enrico Scalas) It and Stratonovich integrals on compound renewal processes: the normal/Poisson case.
    Comm. Nonlinear Sci. Numer. Sim. 15 (2010), 1583-1588.
    [pdf] [arXiv] []
  60. (mit/with Niels Jacob) Extended L p Dirichlet spaces.
    In: Ari Laptev (ed.): Around the Research of Vladimir Maz'ya - Vol. 1: Function Spaces, Springer, Berlin 2009, 221-238.
    [pdf] [arXiv] []
  61. (mit/with Guido Germano, Mauro Politi & Enrico Scalas) Stochastic calculus for uncoupled continuous-time random walks.
    Physical Reviews E 79 (2009) 066102 1-12
    [pdf] [arXiv] []
  62. (mit/with Bjrn Bttcher) Approximation of Feller processes by Markov chains with Lvy increments.
    Stochastics and Dynamics 9 (2009) 71-80.
    [pdf] [arXiv] []
  63. (mit/with T. Uemura) On the Feller property of Dirichlet forms generated by pseudo differential operators.
    Tohoku Math. J. 59 (2007), 401-422
    [pdf] [arXiv] [] [click here for the unabridged version ]
  64. (mit/with N. Jacob) On a Poincar inequality for energy forms in L p .
    Med. J. Math. 4 (2007), 33-44.
    [pdf] [arXiv] []
  65. (mit/with N. Jacob) Towards an L p -potential theory for sub-Markovian semigroups: kernels and capacities,
    Acta Math. Sinica 22 (2006), 1227-1250.
    [pdf] [arXiv] []
  66. (mit/with N. Jacob) Function Spaces as Dirichlet Spaces -- About a Paper by Maz'ya and Nagel
    Z. Analysis Anwendungen 24 (2005), 3-28
    [pdf] [arXiv] []
  67. A note on invariant sets,
    Probab. Math. Stat. 24 (2004), 47-66
    [pdf] [arXiv] [journal] DOI:
  68. (mit/with V.N. Kolokol'tsov & A.E. Tyukov) Estimates for multiple stochastic integrals and stochastic Hamilton-Jacobi equations,
    Revista Mat. Iberoam. 20 (2004), 333-380.
    [pdf] [arXiv] []
  69. (mit/with T. Koscheck, K. Schilling & A. Weyer) Morphological developmment and neurochemical differentiation of cerebellar inhibitory interneurons in microexplant cultures, 
    Neuroscience 116 (2003), 973-984
    [pdf] [arXiv] []
  70. (mit/with V.N. Kolokol'tsov & A.E. Tyukov) Transience and non-explosion of certain stochastic Newtonian systems,
    Elect. J. Probab. 7 (2002), paper 19, 1-19
    [pdf] [arXiv] []
  71. Dirichlet operators and the positive maximum principle,
    Integr. Equ. Oper. Theory 41 (2001), 74-92.
    [pdf] [arXiv] []
  72. (mit/with N. Jacob) Lvy-type processes and pseudo differential operators. In: O. Barndorff-Nielsen, T. Mikosch and S. Resnick (eds.): Lvy processes: theory and applications , Birkhuser, Boston 2001, 139 -167.
    [pdf] [arXiv] [google books] []
  73. (mit/with W. Farkas & N. Jacob) Function spaces related to continuous negative definite functions: $\psi$ - Bessel potential spaces,
    Dissertationes Mathematicae CCCXCIII (2001), 1-62.
    [pdf] [arXiv] []
  74. (mit/with W. Farkas & N. Jacob) Feller semigroups, L p -sub-Markovian semigroups, and applications to pseudo-differential operators with negative definite symbols,
    Forum Math. 13 (2001), 51-90.
    [pdf] [arXiv] []
  75. Function spaces as path spaces of Feller processes,
    Math. Nachr. 217 (2000), 147-174.
    [pdf] [arXiv] [<147::aid-mana147>;2-r]
  76. (mit/with N. Jacob) Fractional derivatives, non-symmetric and time-dependent Dirichlet forms, and the drift form,
    Z. Analysis Anwendungen 19 (2000), 801-830.
    [pdf] [arXiv] []
  77. Sobolev embedding for stochastic processes,
    Expo. Math. 18 (2000), 239-242.
    [pdf] [arXiv] [journal] DOI:
  78. (mit/with N. Jacob) Some Dirichlet spaces obtained by subordinate reflected diffusions,
    Rev. Mat. Iberoam. 15 (1999), 59-91.
    [pdf] [arXiv] []
  79. Growth and Hlder conditions for the sample paths of Feller processes,
    Probab. Theor. Rel. Fields 112 (1998), 565-611.
    [pdf] [arXiv] []
  80. Conservativeness of semigroups generated by pseudo differential operators,
    Potential Analysis 9 (1998), 91-104.
    [pdf] [arXiv] []
  81. Subordination in the sense of Bochner and a related functional calculus,
    J. Austral. Math. Soc. Ser. A 64 (1998), 368 -396.
    [pdf] [arXiv] []
  82. (mit/with N. Jacob) An analytic proof of the Lvy-Khinchin formula on Rn ,
    Publ. Math. Debrecen 53 (1998), 69-89.
    [pdf] [arXiv] [journal] DOI:
  83. Conservativeness and extensions of Feller semigroups,
    Positivity 2(1998), 239 - 256.
    [pdf] [arXiv] []
  84. Feller processes generated by pseudo-differential operators: On the Hausdorff dimension of their sample paths,
    J. Theor. Probab. 11(1998), 303 - 330.
    [pdf] [arXiv] []
  85. On Feller processes with sample paths in Besov spaces,
    Math. Ann. 309(1997), 663 - 675.
    [pdf] [arXiv] []
  86. Comparable processes and the Hausdorff dimension of their sample paths,
    Stochastics and Stochastics Reports 57 (1996), 89-110.
    [pdf] [arXiv] []
  87. (mit/with N. Jacob) Estimates for Feller semigroups generated by pseudodifferential operators,
    in: J. Rkosnk: Function Spaces, Differential Operators and Nonlinear Analysis . Proceedings of the Conference, Paseky nad Jizerou, September 3-9, 1995, Prometheus Publishing House 1996, 27 - 49.
    [pdf] [arXiv] [book chapter] DOI:
  88. On the domain of the generator of a subordinate semigroup,
    in: J. Krl et al. (eds.): Potential Theory - ICPT 94 Proceedings of the International Conference on Potential Theory , Kouty, Czech Republik 1994, de Gruyter, Berlin 1996, 449-462.
    [pdf] [arXiv]  [google books] []
  89. (mit/with N. Jacob) Subordination in the sense of S. Bochner - An approach through pseudo differential operators,
    Math. Nachr. 176(1996), 199 - 231.
    [pdf] [arXiv] []
  90. Zum Pfadverhalten von Markovschen Prozessen, die mit Lvy-Prozessen vergleichbar sind,
    Dissertation Universitt Erlangen 1994.
  91. When does a cdlg process have continuous sample paths?,
    Expo. Math. 12 (1994), 255-261.
    [pdf] [arXiv] [journal] DOI:

Autor: Ren Schilling