caa a22 4500 445331534 CHVBK 20180317142739.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s10208-011-9101-9 doi (NATIONALLICENCE)springer-10.1007/s10208-011-9101-9 Convergence of the Stochastic Euler Scheme for Locally Lipschitz Coefficients [Elektronische Daten] [Martin Hutzenthaler, Arnulf Jentzen] Stochastic differential equations are often simulated with the Monte Carlo Euler method. Convergence of this method is well understood in the case of globally Lipschitz continuous coefficients of the stochastic differential equation. However, the important case of superlinearly growing coefficients has remained an open question. The main difficulty is that numerically weak convergence fails to hold in many cases of superlinearly growing coefficients. In this paper we overcome this difficulty and establish convergence of the Monte Carlo Euler method for a large class of one-dimensional stochastic differential equations whose drift functions have at most polynomial growth. SFoCM, 2011 Euler scheme nationallicence Stochastic differential equations nationallicence Monte Carlo Euler method nationallicence Local Lipschitz condition nationallicence Hutzenthaler Martin LMU Biozentrum, Department Biologie II, University of Munich (LMU), 82152, Planegg-Martinsried, Germany aut Jentzen Arnulf Program in Applied and Computational Mathematics, Princeton University, 08544-1000, Princeton, NJ, USA aut Foundations of Computational Mathematics Springer-Verlag 11/6(2011-12-01), 657-706 1615-3375 11:6<657 2011 11 10208 https://doi.org/10.1007/s10208-011-9101-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10208-011-9101-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Hutzenthaler Martin LMU Biozentrum, Department Biologie II, University of Munich (LMU), 82152, Planegg-Martinsried, Germany aut NATIONALLICENCE 700 1- Jentzen Arnulf Program in Applied and Computational Mathematics, Princeton University, 08544-1000, Princeton, NJ, USA aut NATIONALLICENCE 773 0- Foundations of Computational Mathematics Springer-Verlag 11/6(2011-12-01), 657-706 1615-3375 11:6<657 2011 11 10208 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer