Han, Xiaoying; Kloeden, Peter E.; Sonner, Stefanie Discretisation of global attractors for lattice dynamical systems. (English) Zbl 1466.34021 J. Dyn. Differ. Equations 32, No. 3, 1457-1474 (2020). Reviewer: Oleg Anashkin (Simferopol) MSC: 34A33 34D45 37L60 65L20 PDF BibTeX XML Cite \textit{X. Han} et al., J. Dyn. Differ. Equations 32, No. 3, 1457--1474 (2020; Zbl 1466.34021) Full Text: DOI OpenURL
Doan, T. S.; Huong, P. T.; Kloeden, P. E.; Vu, A. M. Euler-Maruyama scheme for Caputo stochastic fractional differential equations. (English) Zbl 1455.60090 J. Comput. Appl. Math. 380, Article ID 112989, 14 p. (2020). MSC: 60H35 60H20 65C30 PDF BibTeX XML Cite \textit{T. S. Doan} et al., J. Comput. Appl. Math. 380, Article ID 112989, 14 p. (2020; Zbl 1455.60090) Full Text: DOI OpenURL
Kloeden, Peter; Shardlow, Tony Gauss-quadrature method for one-dimensional mean-field SDEs. (English) Zbl 1378.65035 SIAM J. Sci. Comput. 39, No. 6, A2784-A2807 (2017). MSC: 65C30 60H10 34F05 60H35 PDF BibTeX XML Cite \textit{P. Kloeden} and \textit{T. Shardlow}, SIAM J. Sci. Comput. 39, No. 6, A2784--A2807 (2017; Zbl 1378.65035) Full Text: DOI arXiv OpenURL
Asai, Y.; Herrmann, E.; Kloeden, P. E. Stable integration of stiff random ordinary differential equations. (English) Zbl 1273.60079 Stochastic Anal. Appl. 31, No. 2, 293-313 (2013). Reviewer: Melvin D. Lax (Long Beach) MSC: 60H35 60H25 65C30 34F05 65L04 PDF BibTeX XML Cite \textit{Y. Asai} et al., Stochastic Anal. Appl. 31, No. 2, 293--313 (2013; Zbl 1273.60079) Full Text: DOI OpenURL
Wu, Fuke; Mao, Xuerong; Kloeden, Peter E. Discrete Razumikhin-type technique and stability of the Euler-Maruyama method to stochastic functional differential equations. (English) Zbl 1270.65005 Discrete Contin. Dyn. Syst. 33, No. 2, 885-903 (2013). Reviewer: Melvin D. Lax (Long Beach) MSC: 65C30 60H10 60H35 34K50 34K28 45R05 45J05 45D05 60H20 PDF BibTeX XML Cite \textit{F. Wu} et al., Discrete Contin. Dyn. Syst. 33, No. 2, 885--903 (2013; Zbl 1270.65005) Full Text: DOI OpenURL
Hutzenthaler, Martin; Jentzen, Arnulf; Kloeden, Peter E. Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients. (English) Zbl 1256.65003 Ann. Appl. Probab. 22, No. 4, 1611-1641 (2012). Reviewer: Melvin D. Lax (Long Beach) MSC: 65C30 60H10 60H35 34F05 PDF BibTeX XML Cite \textit{M. Hutzenthaler} et al., Ann. Appl. Probab. 22, No. 4, 1611--1641 (2012; Zbl 1256.65003) Full Text: DOI arXiv Euclid OpenURL
Kloeden, Peter E.; Neuenkirch, Andreas; Pavani, Raffaella Multilevel Monte Carlo for stochastic differential equations with additive fractional noise. (English) Zbl 1235.60064 Ann. Oper. Res. 189, 255-276 (2011). MSC: 60H10 65C05 60H35 PDF BibTeX XML Cite \textit{P. E. Kloeden} et al., Ann. Oper. Res. 189, 255--276 (2011; Zbl 1235.60064) Full Text: DOI OpenURL
Hutzenthaler, Martin; Jentzen, Arnulf; Kloeden, Peter E. Strong and weak divergence in finite time of Euler’s method for stochastic differential equations with non-globally Lipschitz continuous coefficients. (English) Zbl 1228.65014 Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 467, No. 2130, 1563-1576 (2011). MSC: 65C30 60H10 60H35 PDF BibTeX XML Cite \textit{M. Hutzenthaler} et al., Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 467, No. 2130, 1563--1576 (2011; Zbl 1228.65014) Full Text: DOI arXiv OpenURL
Jentzen, Arnulf; Kloeden, Peter; Winkel, Georg Efficient simulation of nonlinear parabolic SPDEs with additive noise. (English) Zbl 1223.60050 Ann. Appl. Probab. 21, No. 3, 908-950 (2011). Reviewer: Martin Riedler (Linz) MSC: 60H35 60H15 35R60 65C30 PDF BibTeX XML Cite \textit{A. Jentzen} et al., Ann. Appl. Probab. 21, No. 3, 908--950 (2011; Zbl 1223.60050) Full Text: DOI arXiv OpenURL
Jentzen, Arnulf; Kloeden, Peter E. Overcoming the order barrier in the numerical approximation of stochastic partial differential equations with additive space-time noise. (English) Zbl 1186.65011 Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 465, No. 2102, 649-667 (2009). MSC: 65C30 60H15 PDF BibTeX XML Cite \textit{A. Jentzen} and \textit{P. E. Kloeden}, Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 465, No. 2102, 649--667 (2009; Zbl 1186.65011) Full Text: DOI OpenURL
Garrido-Atienza, María J.; Kloeden, Peter E.; Neuenkirch, Andreas Discretization of stationary solutions of stochastic systems driven by fractional Brownian motion. (English) Zbl 1180.93095 Appl. Math. Optim. 60, No. 2, 151-172 (2009). MSC: 93E03 93B18 93E12 60H10 PDF BibTeX XML Cite \textit{M. J. Garrido-Atienza} et al., Appl. Math. Optim. 60, No. 2, 151--172 (2009; Zbl 1180.93095) Full Text: DOI OpenURL
Kloeden, Peter E.; Neuenkirch, Andreas; Pavani, Raffaella Synchronization of noisy dissipative systems under discretization. (English) Zbl 1232.37032 J. Difference Equ. Appl. 15, No. 8-9, 785-801 (2009). MSC: 37H10 37M05 65C30 PDF BibTeX XML Cite \textit{P. E. Kloeden} et al., J. Difference Equ. Appl. 15, No. 8--9, 785--801 (2009; Zbl 1232.37032) Full Text: DOI OpenURL
Kloeden, P. E.; Valero, J. Attractors of set-valued partial differential equations under discretization. (English) Zbl 1177.65148 IMA J. Numer. Anal. 29, No. 3, 690-711 (2009). Reviewer: Dinh Nho Hao (Hanoi) MSC: 65M60 35K57 37L30 65M12 PDF BibTeX XML Cite \textit{P. E. Kloeden} and \textit{J. Valero}, IMA J. Numer. Anal. 29, No. 3, 690--711 (2009; Zbl 1177.65148) Full Text: DOI OpenURL
Caraballo, T.; Kloeden, P. E.; Neuenkirch, A.; Pavani, R. Synchronization of dissipative systems with additive and linear noise. (English) Zbl 1158.65302 Tammer, Christiane (ed.) et al., Festschrift in celebration of Prof. Dr. Wilfried Grecksch’s 60th birthday. Aachen: Shaker Verlag (ISBN 978-3-8322-7500-6/pbk). Berichte aus der Mathematik, 25-47 (2008). MSC: 65C30 60H10 34F05 60H35 37H10 37M05 34D45 PDF BibTeX XML Cite \textit{T. Caraballo} et al., in: Festschrift in celebration of Prof. Dr. Wilfried Grecksch's 60th birthday. Aachen: Shaker Verlag. 25--47 (2008; Zbl 1158.65302) OpenURL
Halidias, Nikolaos; Kloeden, Peter E. A note on the Euler-Maruyama scheme for stochastic differential equations with a discontinuous monotone drift coefficient. (English) Zbl 1136.65008 BIT 48, No. 1, 51-59 (2008). MSC: 65C30 60H10 60H35 34F05 PDF BibTeX XML Cite \textit{N. Halidias} and \textit{P. E. Kloeden}, BIT 48, No. 1, 51--59 (2008; Zbl 1136.65008) Full Text: DOI OpenURL
Higham, Desmond J.; Kloeden, Peter E. Strong convergence rates for backward Euler on a class of nonlinear jump-diffusion problems. (English) Zbl 1128.65007 J. Comput. Appl. Math. 205, No. 2, 949-956 (2007). Reviewer: Jialin Hong (Beijing) MSC: 65C30 60H10 34F05 60H35 65L06 65L20 PDF BibTeX XML Cite \textit{D. J. Higham} and \textit{P. E. Kloeden}, J. Comput. Appl. Math. 205, No. 2, 949--956 (2007; Zbl 1128.65007) Full Text: DOI OpenURL
Caraballo, T.; Kloeden, P. E. The pathwise numerical approximation of stationary solutions of semilinear stochastic evolution equations. (English) Zbl 1113.60064 Appl. Math. Optimization 54, No. 3, 401-415 (2006). Reviewer: Carles Rovira (Barcelona) MSC: 60H35 60H15 60H25 PDF BibTeX XML Cite \textit{T. Caraballo} and \textit{P. E. Kloeden}, Appl. Math. Optim. 54, No. 3, 401--415 (2006; Zbl 1113.60064) Full Text: DOI Link OpenURL
Caraballo, Tomás; Kloeden, Peter E.; Real, José Discretization of asymptotically stable stationary solutions of delay differential equations with a random stationary delay. (English) Zbl 1125.34064 J. Dyn. Differ. Equations 18, No. 4, 863-880 (2006). Reviewer: Vigirdas Mackevičius (Vilnius) MSC: 34K50 34K28 34K25 60G10 65C20 PDF BibTeX XML Cite \textit{T. Caraballo} et al., J. Dyn. Differ. Equations 18, No. 4, 863--880 (2006; Zbl 1125.34064) Full Text: DOI Link OpenURL
Higham, Desmond J.; Kloeden, Peter E. Convergence and stability of implicit methods for jump-diffusion systems. (English) Zbl 1109.65007 Int. J. Numer. Anal. Model. 3, No. 2, 125-140 (2006). Reviewer: Eckhard Platen (Broadway) MSC: 65C30 65L20 34F05 60H10 60H35 PDF BibTeX XML Cite \textit{D. J. Higham} and \textit{P. E. Kloeden}, Int. J. Numer. Anal. Model. 3, No. 2, 125--140 (2006; Zbl 1109.65007) OpenURL
Higham, Desmond J.; Kloeden, Peter. E. Numerical methods for nonlinear stochastic differential equations with jumps. (English) Zbl 1186.65010 Numer. Math. 101, No. 1, 101-119 (2005). MSC: 65C30 60H10 60H35 34F05 65L20 65L50 PDF BibTeX XML Cite \textit{D. J. Higham} and \textit{Peter. E. Kloeden}, Numer. Math. 101, No. 1, 101--119 (2005; Zbl 1186.65010) Full Text: DOI OpenURL
Kloeden, P. E. Synchronization of discrete time dynamical systems. (English) Zbl 1062.37008 J. Difference Equ. Appl. 10, No. 13-15, 1133-1138 (2004). MSC: 37B25 39A11 37C70 PDF BibTeX XML Cite \textit{P. E. Kloeden}, J. Difference Equ. Appl. 10, No. 13--15, 1133--1138 (2004; Zbl 1062.37008) Full Text: DOI OpenURL
Grüne, L.; Kloeden, P. E. Pathwise approximation of random ordinary differential equations. (English) Zbl 0998.65010 BIT 41, No. 4, 711-721 (2001). Reviewer: Melvin D.Lax (Long Beach) MSC: 65C30 65L06 34F05 65L20 60H10 60H35 65L70 PDF BibTeX XML Cite \textit{L. Grüne} and \textit{P. E. Kloeden}, BIT 41, No. 4, 711--721 (2001; Zbl 0998.65010) Full Text: DOI OpenURL
Cheban, D. N.; Kloeden, P. E.; Schmalfuß, B. Pullback attractors under discretization. (English) Zbl 0963.65139 Fiedler, B. (ed.) et al., International conference on differential equations. Proceedings of the conference, Equadiff ’99, Berlin, Germany, August 1-7, 1999. Vol. 2. Singapore: World Scientific. 1024-1029 (2000). MSC: 65P40 65L06 37C10 37C70 PDF BibTeX XML Cite \textit{D. N. Cheban} et al., in: International conference on differential equations. Proceedings of the conference, Equadiff '99, Berlin, Germany, August 1--7, 1999. Vol. 2. Singapore: World Scientific. 1024--1029 (2000; Zbl 0963.65139) OpenURL
Kloeden, P. E.; Platen, E. Numerical methods for stochastic differential equations. (English) Zbl 0858.65148 Kliemann, Wolfgang (ed.) et al., Nonlinear dynamics and stochastic mechanics. Dedicated to Prof. S. T. Ariaratnam on the occasion of his sixtieth birthday. Boca Raton, FL: CRC Press. CRC Mathematical Modelling Series. 437-461 (1995). Reviewer: M.D.Lax (Long Beach) MSC: 65C99 93E03 93D05 65L07 60H10 65L06 65L05 PDF BibTeX XML Cite \textit{P. E. Kloeden} and \textit{E. Platen}, in: Nonlinear dynamics and stochastic mechanics. Dedicated to Prof. S. T. Ariaratnam on the occasion of his sixtieth birthday. Boca Raton, FL: CRC Press. 437--461 (1995; Zbl 0858.65148) OpenURL
Kloeden, Peter E.; Platen, Eckhard; Schurz, Henri Numerical solution of SDE through computer experiments. Including floppy disk. (English) Zbl 0789.65100 Universitext. Berlin: Springer-Verlag. xiv, 292 p. (1994). Reviewer: M.D.Lax (Long Beach) MSC: 65C99 60-04 60H10 65-01 65L05 34F05 PDF BibTeX XML Cite \textit{P. E. Kloeden} et al., Numerical solution of SDE through computer experiments. Including floppy disk. Berlin: Springer-Verlag (1994; Zbl 0789.65100) Full Text: DOI OpenURL
Kloeden, Peter E.; Platen, Eckhard Numerical solution of stochastic differential equations. (English) Zbl 0752.60043 Applications of Mathematics. 23. Berlin: Springer-Verlag. xxxv, 632 p. (1992). Reviewer: M.D.Lax (Long Beach) MSC: 60H10 65C99 65-02 60-02 PDF BibTeX XML Cite \textit{P. E. Kloeden} and \textit{E. Platen}, Numerical solution of stochastic differential equations. Berlin: Springer-Verlag (1992; Zbl 0752.60043) OpenURL