A

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

Altmayer, Martin ; Neuenkirch, Andreas (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]

Akhtari, Bahareh ; Babolian, Esmail ; Neuenkirch, Andreas (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]

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

Vorschau

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

Altmayer, Martin ; Dereich, Steffen ; Li, Sangmeng ; Müller-Gronbach, Thomas ; Neuenkirch, Andreas ; 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]

B

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

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]

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]

C

Caraballo, Tomás ; Kloeden, Peter E. ; Neuenkirch, Andreas ; 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]

D

Duc, Luu H. ; Garrido-Atienza, Maria J. ; Neuenkirch, Andreas ; 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]

Dereich, Steffen ; Neuenkirch, Andreas ; 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 ; 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]

G

Garrido-Atienza, Maria J. ; Neuenkirch, Andreas ; 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]

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

Garrido-Atienza, Maria J. ; Kloeden, Peter E. ; Neuenkirch, Andreas (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]

H

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

J

Jentzen, Arnulf ; Kloeden, Peter E. ; Neuenkirch, Andreas 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]

Jentzen, Arnulf ; Kloeden, Peter E. ; Neuenkirch, Andreas (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 (2009) A random Euler scheme for Carathéodory differential equations. Journal of Computational and Applied Mathematics Amsterdam [u.a.] 224 1 346-359 [Zeitschriftenartikel]

K

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]

Koch, Stefan ; Neuenkirch, Andreas (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]

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

Vorschau

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]

Kloeden, Peter E. ; Neuenkirch, Andreas (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]

Kloeden, Peter E. ; Neuenkirch, Andreas ; 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 ; 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]

Kloeden, Peter E. ; Neuenkirch, Andreas ; 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]

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

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

M

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

Mickel, Annalena ; Neuenkirch, Andreas (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]

Mickel, Annalena ; Neuenkirch, Andreas (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]

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

Vorschau

N

Neuenkirch, Andreas ; 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]

Neuenkirch, Andreas (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]

Neuenkirch, Andreas ; 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]

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

Neuenkirch, Andreas ; Nourdin, Ivan ; Rößler, Andreas ; Tindel, Samy (2018) Trees and asymptotic developments for fractional stochastic differential equations. Ithaca, NY [Arbeitspapier]

Neuenkirch, Andreas ; 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]

Neuenkirch, Andreas ; Shalaiko, Taras (2016) The order barrier for strong approximation of rough volatility models. Ithaca, NY [Arbeitspapier]

Neuenkirch, Andreas ; 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]

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

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

Neuenkirch, Andreas ; 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]

Neuenkirch, Andreas ; Tindel, Samy ; Unterberger, Jérémie (2009) Discretizing the fractional Levy area. Ithaca, NY [Arbeitspapier]

Neuenkirch, Andreas ; 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]

Neuenkirch, Andreas (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]

Neuenkirch, Andreas ; 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 (2007) Optimal pointwise approximation of stochastic differential equations driven by fractional Brownian motion. Ithaca, NY [Arbeitspapier]

Neuenkirch, Andreas ; 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]

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

Neuenkirch, Andreas (2006) Optimal approximation of stochastic differential equations with additive fractional noise. Aachen 113 [Buch]

P

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]

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]

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

S

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