King's College London Department of Mathematics

Publications
by Markus Riedle

Publications

• SPDEs driven by standard symmetric α-stable cylindrical Lévy processes: existence, Lyapunov functionals and Itô formula (with Gergely Bodó, Ondřey Týbl),
  submitted.

• Stochastic integration with respect to canonical α-stable cylindrical Lévy processes (with Gergely Bodó),
  Electronic Journal of Probability Theory, 27, 2022, paper no. 157, 1-23.

• Stochastic evolution equations driven by cylindrical stable noise (with Tomasz Kosmala),
  Stochastic Processes and their Applications, 149, 2022, 278-307.

• Modelling Lévy space-time white noises (with Matthew Griffiths),
  Journal of the London Mathematical Society, 104(3), 2021, 1452-1474

• Invariant measure for the stochastic Cauchy problem driven by a cylindrical Lévy process (with Umesh Kumar),
  Journal of Mathematical Analysis and Applications, 493(2), 2021, 26pp.

• Variational solutions of stochastic partial differential equations with cylindrical Lévy noise (with Tomasz Kosmala),
  Discrete and Continuous Dynamical Systems - Series B, 26(6), 2021, 2879-2898.

• Stochastic integration with respect to cylindrical Lévy processes by p-summing operators (with Tomasz Kosmala),
  Journal of Theoretical Probability, 34, 2021, 477- 497.

• The stochastic Cauchy problem driven by a cylindrical Lévy process (with Umesh Kumar),
  Electronic Journal of Probability, 25, 2020, paper no. 10, 26pp.

• Stable cylindrical Lévy processes and the stochastic Cauchy problem,
  Electronic Communications in Probability, 2018, Vol. 23, paper no. 36, 1-12.

• Large deviations for stochastic heat equations with memory driven by Lévy-type noise (with Jianliang Zhai),
  Discrete and Continuous Dynamical Systems - Series A, 38(4), 2018, 1983-2005.

• Stochastic integration with respect to cylindrical Lévy processes (with A. Jakubowski),
  Annals of Probability, 45(6B), 2017, 4273-4306.

• Copulas in Hilbert spaces (with E. Hausenblas),
  Stochastics, 89(1), 2017, 222-239.

• Ornstein-Uhlenbeck processes driven by cylindrical Lévy processes,
  Potential Analysis, 42, 2015, 809-838.

• Non-standard Skorokhod convergence of Lévy-driven convolution integrals in Hilbert spaces (with I. Pavlyukevich),
  Stochastic Analysis and Applications, 33, 2015, 271-305.

• Radonifying operators and infinitely divisible Wiener integrals,
  invited article, Theory of Stochastic Processes, 19(35), 2014, 90-103.

• Stochastic integration with respect to cylindrical Lévy processes in Hilbert spaces: an L^2 approach,
  Infinite Dimensional Analysis, Quantum Probability and Related Topics, 17, 2014.

• Cylindrical Fractional Brownian Motion in Banach Spaces (with E. Issoglio),
  Stochastic Processes and Applications 124, 2014, 3507-3534.

• Bubbles and crashes in the Black-Scholes model with delay (with J. A. D. Appleby, C. Swords),
  Finance and Stochastics 17, 2013, 1 - 30.

• Infinitely divisible cylindrical measures on Banach spaces,
  Studia Mathematica 207, 2011, 235 - 256.

• Cylindrical Wiener processes,
  Séminaire de probabilités XLIII, Berlin: Springer. Lecture Notes in Mathematics Vol. 2006, 2011, 191 - 214.

• Cylindrical Lévy processes in Banach spaces (with D. Applebaum),
  Proceedings of the London Mathematical Society 101, 2010, 697 - 726.

• Stochastic Volterra differential equations in weighted spaces (with J. A. D. Appleby),
  Journal of Integral Equations and Applications 22, 2010, 1 - 18.

• Stochastic integration for Lévy processes with values in Banach spaces (with O. van Gaans),
  Stochastic Processes and Their Applications 119, 2009, 1952 - 1974.

• Geometric Brownian motion with delay: mean square characterization (with J. A. D. Appleby, X. Mao),
  Proceedings of the American Mathematical Society 137, 2009, 339 - 348.

• On asymptotic stability of linear stochastic Volterra difference equations with respect to a fading perturbation (with J. A. D. Appleby, A. Rodkina),
  Adv. Stud. Pure Math. 53, 2009.

• Solutions of affine stochastic functional differential equations in the state space,
  Journal of Evolution Equations 8, 2008, 71 - 97.

• A semigroup approach to stochastic delay equations in spaces of continuous functions (with J. M. A. M. van Neerven),
  Semigroup forum 74, 2007, 227 - 239.

• On Émery's inequality and a variation-of-constants formula (with M. Reiß,O. van Gaans) ,
  Stochastic analysis and applications 25, 2007, 353 - 379.

• Delay differential equations driven by Lévy process: stationarity and Feller properties (with M. Reiß, O. van Gaans) ,
  Stochastic processes and their applications 116, 2006, 1409 - 1432.

• Almost sure asymptotic stability of Volterra integro-differential equations with fading perturbations, (with J. A. D. Appleby),
  Stochastic analysis and applications 24, 2006, 813 - 826.

• Lyapunov exponents for linear delay equations in arbitrary phase spaces,
  Integral equations and operator theory 54, 2006, 259 - 278.

• Mean square stability of stochastic Volterra integro-differential equations (with X. Mao),
  Systems and Control Letters 55, 2006, 459 - 465.

• Variance estimation in the change analysis of a linear regression model (with J. Steinebach),
  Metrika 54(2), 2001, 139 - 157.