Zeitschriftenartikel

Mickel, Annalena ; Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 (2023) The weak convergence order of two Euler-type discretization schemes for the log-Heston model. IMA Journal of Numerical Analysis : IMAJNA Oxford 43 6 3326-3356 [Zeitschriftenartikel]

Mickel, Annalena ; Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 (2023) Sharp L1-approximation of the log-Heston stochastic differential equation by Euler-type methods. The Journal of Computational Finance London 26 4 67-100 [Zeitschriftenartikel]

Klingert, Sonja ; Lee, Jong-Won (2022) Using real mobility patterns to assess the impact of 100% electrified mobility in a German city. Energy Informatics Cham 5 Article 32 1-24 [Zeitschriftenartikel]

Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 ; Szölgyenyi, Michaela (2021) The Euler-Maruyama scheme for SDEs with irregular drift: convergence rates via reduction to a quadrature problem. IMA Journal of Numerical Analysis : IMAJNA Oxford 41 2 1164-1196 [Zeitschriftenartikel]

Mickel, Annalena ; Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 (2021) The weak convergence rate of two semi-exact discretization schemes for the Heston model. Risks : Open Access Journal Basel 9 1 Article 23 [Zeitschriftenartikel]

Koch, Stefan ; Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 (2019) The Mandelbrot-van Ness fractional Brownian motion is infinitely differentiable with respect to its Hurst parameter. Discrete and Continuous Dynamical Systems : DCDS. Series B Springfield, MO 24 8 3865-3880 [Zeitschriftenartikel]

Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 ; Szölgyenyi, Michaela ; Szpruch, Lukasz (2019) An adaptive Euler-Maruyama scheme for stochastic differential equations with discontinuous drift and its convergence analysis. SIAM Journal on Numerical Analysis Philadelphia, PA 57 1 378-403 [Zeitschriftenartikel]

Göttlich, Simone ORCID: 0000-0002-8512-4525 ; Lux, Kerstin ; Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 (2019) The Euler scheme for stochastic differential equations with discontinuous drift coefficient: a numerical study of the convergence rate. Advances in Difference Equations : ADE Cham 2019 Article 429 1-21 [Zeitschriftenartikel]

Vorschau

Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 ; Parczewski, Peter (2018) Optimal approximation of skorohod integrals. Journal of Theoretical Probability New York, NY [u.a.] 31 1 206-231 [Zeitschriftenartikel]

Garrido-Atienza, Maria J. ; Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 ; Schmalfuß, Björn (2018) Asymptotical stability of differential equations driven by Hölder continuous paths. Journal of Dynamics and Differential Equations New York, NY [u.a.] 30 1 359-377 [Zeitschriftenartikel]

Duc, Luu H. ; Garrido-Atienza, Maria J. ; Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 ; Schmalfuß, Björn (2018) Exponential stability of stochastic evolution equations driven by small fractional Brownian motion with Hurst parameter in (1/2,1). Journal of Differential Equations Orlando, FL [u.a.] 264 2 1119-1145 [Zeitschriftenartikel]

Koch, Stefan (2018) Directional Malliavin derivatives: A characterisation of independence and a generalised chain rule. Communications on Stochastic Analysis Baton Rouge, LA 12 2 137-156 [Zeitschriftenartikel]

Bender, Christian ; Parczewski, Peter (2018) Discretizing Malliavin calculus. Stochastic Processes and Their Applications Amsterdam [u.a.] 128 8 2489 - 2537 [Zeitschriftenartikel]

Altmayer, Martin ; Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 (2017) Discretising the Heston model: an analysis of the weak convergence rate. IMA Journal of Numerical Analysis : IMAJNA Oxford 37 4 1930-1960 [Zeitschriftenartikel]

Parczewski, Peter (2017) Extensions of the Hitsuda–Skorokhod integral. Communications on Stochastic Analysis Baton Rouge, LA 11 4 479-490 [Zeitschriftenartikel]

Parczewski, Peter (2017) The self-normalized Donsker theorem revisited. Modern Stochastics: Theory and Applications Vilnius 4 3 189-198 [Zeitschriftenartikel]

Parczewski, Peter (2017) Optimal approximation of Skorohod integrals - examples with substandard rates. Communications on Stochastic Analysis Baton Rouge, LA 11 1 43-61 [Zeitschriftenartikel]

Parczewski, Peter (2017) Donsker-type theorems for correlated geometric fractional Brownian motions and related processes. Electronic Communications in Probability : ECP Seattle, WA 22 Paper 55 1-13 [Zeitschriftenartikel]

Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 ; Shalaiko, Taras (2016) The maximum rate of convergence for the approximation of the fractional Lévy area at a single point. Journal of Complexity Amsterdam 33 107-117 [Zeitschriftenartikel]

Altmayer, Martin ; Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 (2015) Multilevel Monte Carlo quadrature of discontinuous payoffs in the generalized Heston model using Malliavin integration by parts. SIAM Journal on Financial Mathematics : SIFIN Philadelphia, Pa. 6 1 22-52 [Zeitschriftenartikel]

Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 ; Shalaiko, Taras (2015) The relation between mixed and rough SDEs and its application to numerical methods. Stochastic Analysis and Applications Philadelphia, Pa. 33 5 927-942 [Zeitschriftenartikel]

Akhtari, Bahareh ; Babolian, Esmail ; Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 (2015) An Euler scheme for stochastic delay differential equations on unbounded domains: pathwise convergence. Discrete and Continuous Dynamical Systems : DCDS. Series B Springfield, Mo. 20 1 23-38 [Zeitschriftenartikel]

Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 ; Szpruch, Lukasz (2014) First order strong approximations of scalar SDEs defined in a domain. Numerische Mathematik Berlin [u.a.] 128 1 103-136 [Zeitschriftenartikel]

Parczewski, Peter (2014) A Wick functional limit theorem. Probability and Mathematical Statistics Wrocław 34 1 127-145 [Zeitschriftenartikel]

Parczewski, Peter (2014) A fractional Donsker theorem. Stochastic Analysis and Applications Philadelphia, PA 32 2 328-347 [Zeitschriftenartikel]

Hinrichs, Aicke ; Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 ; Novak, Erich (2014) Guest editors' preface. Journal of Complexity Amsterdam [u.a.] 30 2 1 [Zeitschriftenartikel]

Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 ; Tindel, Samy (2014) A least square-type procedure for parameter estimation in stochastic differential equations with additive fractional noise. Statistical Inference for Stochastic Processes Dordrecht [u.a.] 17 1 99-120 [Zeitschriftenartikel]

Dereich, Steffen ; Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 ; Szpruch, Lukasz (2012) An Euler-type method for the strong approximation of the Cox-Ingersoll-Ross process. Proceedings / Section A, Mathematics Edinburgh 468 1105-1115 [Zeitschriftenartikel]

Deya, Aurélien ; Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 ; Tindel, Samy (2012) A Milstein-type scheme without Lévy area terms for SDEs driven by fractional Brownian motion. Annales de l'Institut Henri Poincaré. B, Probabilité et statistiques Bethesda, Md. 48 2 518-550 [Zeitschriftenartikel]

Kloeden, Peter E. ; Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 ; Pavani, Raffaella (2011) Multilevel Monte Carlo for stochastic differential equations with additive fractional noise. Annals of Operations Research New York, NY [u.a.] 189 1 255-276 [Zeitschriftenartikel]

Kloeden, Peter E. ; Lord, Gabriel J. ; Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 ; Shardlow, Tony (2011) The exponential integrator scheme for stochastic partial differential equations: Pathwise error bounds. Journal of Computational and Applied Mathematics Amsterdam [u.a.] 235 5 1245-1260 [Zeitschriftenartikel]

Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 ; Tindel, Samy ; Unterberger, Jérémie (2010) Discretizing the fractional Lévy area. Stochastic Processes and Their Applications Amsterdam [u.a.] 120 2 223-254 [Zeitschriftenartikel]

Bender, Christian ; Parczewski, Peter (2010) Approximating a geometric fractional Brownian motion and related processes via discrete Wick calculus. Bernoulli : Official Journal of the Bernoulli Society for Mathematical Statistics and Probability London 16 2 389-417 [Zeitschriftenartikel]

Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 ; Nourdin, Ivan ; Rößler, Andreas ; Tindel, Samy (2009) Trees and asymptotic expansions for fractional stochastic differential equations. Annales de l'Institut Henri Poincaré. B, Probabilité et statistiques Bethesda, MD 45 1 157-174 [Zeitschriftenartikel]

Garrido-Atienza, Maria J. ; Kloeden, Peter E. ; Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 (2009) Discretization of stationary solutions of stochastic systems driven by fractional Brownian motion. Applied Mathematics and Optimization New York, NY ; Heidelberg ; Berlin 60 2 151-172 [Zeitschriftenartikel]

Jentzen, Arnulf ; Kloeden, Peter E. ; Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 (2009) Pathwise approximation of stochastic differential equations on domains: higher order convergence rates without global Lipschitz coefficients. Numerische Mathematik Berlin [u.a.] 112 1 41-64 [Zeitschriftenartikel]

Jentzen, Arnulf ; Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 (2009) A random Euler scheme for Carathéodory differential equations. Journal of Computational and Applied Mathematics Amsterdam [u.a.] 224 1 346-359 [Zeitschriftenartikel]

Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 ; Zähle, Henryk (2009) Asymptotic error distribution of the Euler method for SDEs with non-Lipschitz coefficients. Monte Carlo Methods and Applications Berlin [u.a.] 15 4 333-351 [Zeitschriftenartikel]

Kloeden, Peter E. ; Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 ; Pavani, Raffaella (2009) Synchronization of noisy dissipative systems under discretization. Journal of Difference Equations and Applications London [u.a.] 15 8/9 785-801 [Zeitschriftenartikel]

Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 (2008) Optimal pointwise approximation of stochastic differential equations driven by fractional Brownian motion. Stochastic Processes and Their Applications Amsterdam [u.a.] 118 12 2294-2333 [Zeitschriftenartikel]

Kloeden, Peter E. ; Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 ; Caraballo, Tomás (2008) Synchronization of systems with multiplicative noise. Stochastics and Dynamics : SD Singapore [u.a.] 8 1 139-154 [Zeitschriftenartikel]

Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 ; Nourdin, Ivan ; Tindel, Samy (2008) Delay equations driven by rough paths. Electronic Journal of Probability : EJP Seattle, WA 13 Paper 67 2031-2068 [Zeitschriftenartikel]

Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 ; Nourdin, Ivan (2007) Exact rate of convergence of some approximation schemes associated to SDEs driven by a fractional Brownian motion. Journal of Theoretical Probability New York, NY [u.a.] 20 4 871-899 [Zeitschriftenartikel]

Kloeden, Peter E. ; Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 (2007) The pathwise convergence of approximation schemes for stochastic differential equations. LMS Journal of Computation and Mathematics London 10 1 235-253 [Zeitschriftenartikel]

Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 (2006) Optimal approximation of SDE's with additive fractional noise. Journal of Complexity Amsterdam [u.a.] 22 4 459-474 [Zeitschriftenartikel]

Buch

Altmayer, Martin (2015) Quadrature of discontinuous SDE functionals using Malliavin integration by parts. München [Buch]

Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 (2006) Optimal approximation of stochastic differential equations with additive fractional noise. Aachen 113 [Buch]

Buchkapitel

Altmayer, Martin ; Dereich, Steffen ; Li, Sangmeng ; Müller-Gronbach, Thomas ; Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 ; Ritter, Klaus ; Yaroslavtseva, Larissa (2014) Constructive quantization and multilevel algorithms for quadrature of stochastic differential equations. Dahlke, Stephan Extraction of Quantifiable Information from Complex Systems Lecture Notes in Computational Science and Engineering Cham 102 109-132 [Buchkapitel]

Kloeden, Peter E. ; Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 (2013) Convergence of numerical methods for stochastic differential equations in mathematical finance. Gerstner, Thomas Recent Developments in Computational Finance Interdisciplinary Mathematical Sciences New Jersey, NJ [u.a.] 14 49-80 [Buchkapitel]

Bender, Christian ; Parczewski, Peter (2012) On the connection between discrete and continuous Wick calculus with an application to the fractional Black-Scholes model. Cohen, Samuel N. Stochastic processes, finance and control : a Festschrift in honor of Robert J. Elliott Advances in statistics, probability and actuarial science Hackensack, NJ [u.a.] 1 3-40 [Buchkapitel]

Caraballo, Tomás ; Kloeden, Peter E. ; Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 ; Pavani, Raffaella (2008) Synchronization of dissipative systems with additive and linear noise. Tammer, Christiane Festschrift in celebration of Prof. Dr. Wilfried Grecksch's 60th birthday Interdisciplinary Mathematical Sciences Aachen 25-47 [Buchkapitel]

Dissertation

Mickel, Annalena (2023) Weak and strong approximation of the Log-Heston model by Euler-Type methods and related topics. Mannheim [Dissertation]

Madensoy, Mehmet (2020) Change points and uniform confidence for spot volatility. Mannheim [Dissertation]

Vorschau

Koch, Stefan (2019) Sensitivity results in stochastic analysis. Mannheim [Dissertation]

Vorschau

Altmayer, Martin (2015) Quadrature of discontinuous SDE functionals using Malliavin integration by parts. Mannheim [Dissertation]

Vorschau

Schneider, Georg Hubert (2013) Lagrange interpolation and quasi-interpolation using trivariate splines on a uniform partition. Mannheim [Dissertation]

Parczewski, Peter (2013) A Wick functional limit theorem and applications to fractional Brownian motion. Saarbrücken [Dissertation]

Konferenzveröffentlichung

Jentzen, Arnulf ; Kloeden, Peter E. ; Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 Pathwise convergence of numerical schemes for random and stochastic differential equations. Cucker, Felipe London Mathematical Society Lecture Note Series 363 140-161 In: Foundations of Computational Mathematics, Hong Kong 2008 (2009) Cambridge Foundations of Computational Mathematics, Hong Kong 2008 (Hong Kong, China) [Konferenzveröffentlichung]

Arbeitspapier

Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 ; Szölgyenyi, Michaela (2019) The Euler-Maruyama scheme for SDEs with irregular drift: Convergence rates via reduction to a quadrature problem. Ithaca, NY [Arbeitspapier]

Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 ; Nourdin, Ivan ; Rößler, Andreas ; Tindel, Samy (2018) Trees and asymptotic developments for fractional stochastic differential equations. Ithaca, NY [Arbeitspapier]

Göttlich, Simone ORCID: 0000-0002-8512-4525 ; Lux, Kerstin ; Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 (2017) The Euler scheme for stochastic differential equations with discontinuous drift coefficient: A numerical study of the convergence rate. Ithaca, NY [Arbeitspapier]

Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 ; Shalaiko, Taras (2016) The order barrier for strong approximation of rough volatility models. Ithaca, NY [Arbeitspapier]

Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 ; Tindel, Samy ; Unterberger, Jérémie (2009) Discretizing the fractional Levy area. Ithaca, NY [Arbeitspapier]

Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 (2007) Optimal pointwise approximation of stochastic differential equations driven by fractional Brownian motion. Ithaca, NY [Arbeitspapier]

Rezension

Neuenkirch, Andreas ORCID: 0000-0002-0419-1225 (2021) D. Higham, P. Kloeden: "An introduction to the numerical simulation of stochastic differential equations". Jahresbericht der Deutschen Mathematiker-Vereinigung Heidelberg 124 119-122 [Rezension]