Drift-preserving numerical integrators for stochastic Hamiltonian systems
The paper deals with numerical discretizations of separable nonlinear Hamiltonian systems with additive noise. For such problems, the expected value of the total energy, along the exact solution, drifts linearly with time. We present and analyze a time integrator having the same property for all tim...
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| Published in | Advances in computational mathematics Vol. 46; no. 2 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
2020
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1019-7168 1572-9044 1572-9044 |
| DOI | 10.1007/s10444-020-09771-5 |
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| Abstract | The paper deals with numerical discretizations of separable nonlinear Hamiltonian systems with additive noise. For such problems, the expected value of the total energy, along the exact solution, drifts linearly with time. We present and analyze a time integrator having the same property for all times. Furthermore, strong and weak convergence of the numerical scheme along with efficient multilevel Monte Carlo estimators are studied. Finally, extensive numerical experiments illustrate the performance of the proposed numerical scheme. |
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| AbstractList | The paper deals with numerical discretizations of separable nonlinear Hamiltonian systems with additive noise. For such problems, the expected value of the total energy, along the exact solution, drifts linearly with time. We present and analyze a time integrator having the same property for all times. Furthermore, strong and weak convergence of the numerical scheme along with efficient multilevel Monte Carlo estimators are studied. Finally, extensive numerical experiments illustrate the performance of the proposed numerical scheme. |
| ArticleNumber | 27 |
| Author | D’Ambrosio, Raffaele Chen, Chuchu Cohen, David Lang, Annika |
| Author_xml | – sequence: 1 givenname: Chuchu surname: Chen fullname: Chen, Chuchu organization: State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences – sequence: 2 givenname: David orcidid: 0000-0001-6490-1957 surname: Cohen fullname: Cohen, David email: david.cohen@umu.se organization: Department of Mathematics and Mathematical Statistics, Umeå University – sequence: 3 givenname: Raffaele surname: D’Ambrosio fullname: D’Ambrosio, Raffaele organization: Department of Information Engineering and Computer Science and Mathematics, University of L’Aquila – sequence: 4 givenname: Annika surname: Lang fullname: Lang, Annika organization: Department of Mathematical Sciences, Chalmers University of Technology & University of Gothenburg |
| BackLink | https://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-167824$$DView record from Swedish Publication Index https://gup.ub.gu.se/publication/292400$$DView record from Swedish Publication Index https://research.chalmers.se/publication/516178$$DView record from Swedish Publication Index |
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| Cites_doi | 10.1016/j.apnum.2014.08.003 10.1090/S0025-5718-2014-02805-6 10.1007/s10543-016-0608-y 10.1016/j.cam.2017.11.043 10.1007/BF02440162 10.1007/978-3-662-10063-9 10.1137/12087030X 10.1007/s10543-004-5240-6 10.1088/1751-8113/41/4/045206 10.4208/jcm.1701-m2016-0525 10.1007/s11075-013-9796-6 10.1016/j.jcp.2012.10.015 10.1007/s10543-014-0507-z 10.1016/j.cam.2012.03.007 10.1007/s10543-011-0310-z 10.1287/opre.1070.0496 10.1007/s10543-014-0474-4 10.1016/j.cam.2018.07.006 10.1007/978-3-662-12616-5 10.1137/090771880 10.1016/j.matcom.2012.02.004 10.1016/j.apnum.2004.02.003 10.1016/j.cam.2012.03.026 10.1007/s00211-011-0426-8 10.4310/CMS.2014.v12.n8.a7 10.1007/s10543-016-0620-2 10.1007/s10543-016-0614-0 10.1137/15M101049X 10.1090/S0025-5718-09-02220-0 10.1098/rsta.1999.0363 10.1137/15M1020861 10.1007/3-540-45346-6_5 10.1007/978-3-319-33507-0_25 10.1007/s10444-020-09771-5 10.1016/j.jcp.2020.109382 |
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| Keywords | Weak convergence 65C20 Stochastic differential equations Strong convergence 60H10 65C30 Energy Trace formula Multilevel Monte Carlo Numerical schemes Stochastic Hamiltonian systems 60H35 |
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| References | Hairer (CR22) 2010; 5 Cohen (CR10) 2012; 82 Zhou, Zhang, Hong, Song (CR42) 2016; 56 Anton, Cohen (CR1) 2018; 36 Burrage, Burrage (CR6) 2012; 236 Strømmen Melbø, Higham (CR40) 2004; 51 de la Cruz, Jimenez, Zubelli (CR17) 2017; 57 Senosiain, Tocino (CR39) 2015; 55 CR16 Wu, Wang, Shi (CR41) 2013; 235 Kloeden, Platen (CR30) 1992 Quispel, McLaren (CR37) 2008; 41 CR11 Faou, Lelièvre (CR19) 2009; 78 CR32 Brugnano, Gurioli, Iavernaro (CR3) 2018; 335 Schurz (CR38) 2008; 1 McLachlan, Quispel, Robidoux (CR33) 1999; 357 Faou, Hairer, Pham (CR18) 2004; 51 Burrage, Burrage (CR5) 2014; 65 Hong, Zhai, Zhang (CR28) 2011; 49 Cohen, Dujardin (CR12) 2014; 12 Hong, Xu, Wang (CR27) 2015; 87 Anton, Cohen, Larsson, Wang (CR2) 2016; 54 Cohen, Hairer (CR13) 2011; 51 Giles (CR20) 2008; 56 CR9 Celledoni, Owren, Sun (CR7) 2014; 83 Gonzalez (CR21) 1996; 6 Chen, Cohen, Hong (CR8) 2016; 13 CR25 Miyatake (CR35) 2014; 54 Iavernaro, Trigiante (CR29) 2009; 4 Cohen, Sigg (CR15) 2012; 121 Cohen, Larsson, Sigg (CR14) 2013; 51 Han, Ma, Ding (CR24) 2019; 346 Milstein, Tretyakov (CR34) 2004 Kojima (CR31) 2016; 56 Hairer, Lubich, Wanner (CR23) 2006 Miyatake, Butcher (CR36) 2016; 54 Brugnano, Iavernaro (CR4) 2012; 236 Hong, Scherer, Wang (CR26) 2006; 14 J Hong (9771_CR28) 2011; 49 E Hairer (9771_CR22) 2010; 5 MJ Senosiain (9771_CR39) 2015; 55 W Zhou (9771_CR42) 2016; 56 GN Milstein (9771_CR34) 2004 H Schurz (9771_CR38) 2008; 1 D Cohen (9771_CR15) 2012; 121 9771_CR25 D Cohen (9771_CR10) 2012; 82 D Cohen (9771_CR13) 2011; 51 PM Burrage (9771_CR5) 2014; 65 D Cohen (9771_CR12) 2014; 12 D Cohen (9771_CR14) 2013; 51 Y Miyatake (9771_CR35) 2014; 54 Y Miyatake (9771_CR36) 2016; 54 E Celledoni (9771_CR7) 2014; 83 H Kojima (9771_CR31) 2016; 56 X Wu (9771_CR41) 2013; 235 PM Burrage (9771_CR6) 2012; 236 R Anton (9771_CR2) 2016; 54 L Brugnano (9771_CR3) 2018; 335 J Hong (9771_CR27) 2015; 87 F Iavernaro (9771_CR29) 2009; 4 PE Kloeden (9771_CR30) 1992 E Faou (9771_CR18) 2004; 51 O Gonzalez (9771_CR21) 1996; 6 R Anton (9771_CR1) 2018; 36 E Hairer (9771_CR23) 2006 RI McLachlan (9771_CR33) 1999; 357 9771_CR16 9771_CR9 H de la Cruz (9771_CR17) 2017; 57 M Han (9771_CR24) 2019; 346 GRW Quispel (9771_CR37) 2008; 41 AH Strømmen Melbø (9771_CR40) 2004; 51 C Chen (9771_CR8) 2016; 13 J Hong (9771_CR26) 2006; 14 E Faou (9771_CR19) 2009; 78 L Brugnano (9771_CR4) 2012; 236 9771_CR11 9771_CR32 MB Giles (9771_CR20) 2008; 56 |
| References_xml | – volume: 87 start-page: 38 year: 2015 end-page: 52 ident: CR27 article-title: Preservation of quadratic invariants of stochastic differential equations via Runge-Kutta methods publication-title: Appl. Numer Math. doi: 10.1016/j.apnum.2014.08.003 – volume: 83 start-page: 1689 issue: 288 year: 2014 end-page: 1700 ident: CR7 article-title: The minimal stage, energy preserving Runge-Kutta method for polynomial Hamiltonian systems is the averaged vector field method publication-title: Math. Comp. doi: 10.1090/S0025-5718-2014-02805-6 – volume: 56 start-page: 1317 issue: 4 year: 2016 end-page: 1337 ident: CR31 article-title: Invariants preserving schemes based on explicit Runge–Kutta methods publication-title: BIT doi: 10.1007/s10543-016-0608-y – volume: 335 start-page: 51 year: 2018 end-page: 73 ident: CR3 article-title: Analysis of energy and quadratic invariant preserving (EQUIP) methods publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2017.11.043 – ident: CR16 – volume: 6 start-page: 449 issue: 5 year: 1996 end-page: 467 ident: CR21 article-title: Time integration and discrete Hamiltonian systems publication-title: J. Nonlinear Sci. doi: 10.1007/BF02440162 – year: 2004 ident: CR34 publication-title: Stochastic Numerics for Mathematical Physics. Scientific Computation doi: 10.1007/978-3-662-10063-9 – volume: 51 start-page: 204 issue: 1 year: 2013 end-page: 222 ident: CR14 article-title: A trigonometric method for the linear stochastic wave equation publication-title: SIAM J. Numer Anal. doi: 10.1137/12087030X – volume: 51 start-page: 699 issue: 44 year: 2004 end-page: 709 ident: CR18 article-title: Energy conservation with non-symplectic methods: Examples and counter-examples publication-title: BIT doi: 10.1007/s10543-004-5240-6 – volume: 41 start-page: 045206, 7 issue: 4 year: 2008 ident: CR37 article-title: A new class of energy-preserving numerical integration methods publication-title: J. Phys. A doi: 10.1088/1751-8113/41/4/045206 – volume: 36 start-page: 276 issue: 2 year: 2018 end-page: 309 ident: CR1 article-title: Exponential integrators for stochastic Schrödinger equations driven by Itô noise publication-title: J. Comput. Math. doi: 10.4208/jcm.1701-m2016-0525 – volume: 65 start-page: 519 issue: 3 year: 2014 end-page: 532 ident: CR5 article-title: Structure-preserving Runge-Kutta methods for stochastic Hamiltonian equations with additive noise publication-title: Numer. Algor. doi: 10.1007/s11075-013-9796-6 – volume: 235 start-page: 587 year: 2013 end-page: 605 ident: CR41 article-title: Efficient energy-preserving integrators for oscillatory Hamiltonian systems publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2012.10.015 – volume: 55 start-page: 515 issue: 2 year: 2015 end-page: 529 ident: CR39 article-title: A review on numerical schemes for solving a linear stochastic oscillator publication-title: BIT doi: 10.1007/s10543-014-0507-z – volume: 1 start-page: 353 issue: 2 year: 2008 end-page: 363 ident: CR38 article-title: Analysis and discretization of semi-linear stochastic wave equations with cubic nonlinearity and additive space-time noise publication-title: Discrete Contin. Dyn. Syst. Ser. S – volume: 4 start-page: 87 issue: 1-2 year: 2009 end-page: 101 ident: CR29 article-title: High-order symmetric schemes for the energy conservation of polynomial Hamiltonian problems publication-title: J. Numer. Anal. Ind. Appl Math. – ident: CR25 – volume: 236 start-page: 3920 year: 2012 end-page: 3930 ident: CR6 article-title: Low rank Runge-Kutta methods, symplecticity and stochastic Hamiltonian problems with additive noise publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2012.03.007 – volume: 51 start-page: 91 issue: 1 year: 2011 end-page: 101 ident: CR13 article-title: Linear energy-preserving integrators for Poisson systems publication-title: BIT doi: 10.1007/s10543-011-0310-z – volume: 56 start-page: 607 issue: 3 year: 2008 end-page: 617 ident: CR20 article-title: Multilevel Monte Carlo path simulation publication-title: Oper. Res. doi: 10.1287/opre.1070.0496 – year: 2006 ident: CR23 publication-title: Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations, 2nd edn, Volume 31 of Springer Series in Computational Mathematics – volume: 54 start-page: 777 issue: 3 year: 2014 end-page: 799 ident: CR35 article-title: An energy-preserving exponentially-fitted continuous stage Runge-Kutta method for Hamiltonian systems publication-title: BIT doi: 10.1007/s10543-014-0474-4 – volume: 346 start-page: 575 year: 2019 end-page: 593 ident: CR24 article-title: High-order stochastic symplectic partitioned Runge–Kutta methods for stochastic Hamiltonian systems with additive noise publication-title: Appl. Math. Comput. doi: 10.1016/j.cam.2018.07.006 – year: 1992 ident: CR30 publication-title: Numerical Solution of Stochastic Differential Equations, Volume 23 of Applications of Mathematics doi: 10.1007/978-3-662-12616-5 – volume: 49 start-page: 2017 issue: 5 year: 2011 end-page: 2038 ident: CR28 article-title: Discrete gradient approach to stochastic differential equations with a conserved quantity publication-title: SIAM J. Numer. Anal. doi: 10.1137/090771880 – volume: 82 start-page: 1478 issue: 8 year: 2012 end-page: 1495 ident: CR10 article-title: On the numerical discretisation of stochastic oscillators publication-title: Math. Comput. Simul. doi: 10.1016/j.matcom.2012.02.004 – volume: 51 start-page: 89 issue: 1 year: 2004 end-page: 99 ident: CR40 article-title: Numerical simulation of a linear stochastic oscillator with additive noise publication-title: Appl. Numer. Math. doi: 10.1016/j.apnum.2004.02.003 – volume: 236 start-page: 3905 issue: 16 year: 2012 end-page: 3919 ident: CR4 article-title: Line integral methods which preserve all invariants of conservative problems publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2012.03.026 – volume: 121 start-page: 1 issue: 1 year: 2012 end-page: 29 ident: CR15 article-title: Convergence analysis of trigonometric methods for stiff second-order stochastic differential equations publication-title: Numer. Math. doi: 10.1007/s00211-011-0426-8 – volume: 12 start-page: 1523 issue: 8 year: 2014 end-page: 1539 ident: CR12 article-title: Energy-preserving integrators for stochastic Poisson systems publication-title: Commun. Math Sci. doi: 10.4310/CMS.2014.v12.n8.a7 – volume: 57 start-page: 123 issue: 1 year: 2017 end-page: 151 ident: CR17 article-title: Locally linearized methods for the simulation of stochastic oscillators driven by random forces publication-title: BIT doi: 10.1007/s10543-016-0620-2 – volume: 13 start-page: 435 issue: 3 year: 2016 end-page: 456 ident: CR8 article-title: Conservative methods for stochastic differential equations with a conserved quantity publication-title: Int. J. Numer. Anal Model. – ident: CR11 – ident: CR9 – ident: CR32 – volume: 56 start-page: 1497 issue: 4 year: 2016 end-page: 1518 ident: CR42 article-title: Projection methods for stochastic differential equations with conserved quantities publication-title: BIT doi: 10.1007/s10543-016-0614-0 – volume: 5 start-page: 73 issue: 1-2 year: 2010 end-page: 84 ident: CR22 article-title: Energy-preserving variant of collocation methods publication-title: J. Numer. Anal. Ind. Appl. Math. – volume: 54 start-page: 1093 issue: 2 year: 2016 end-page: 1119 ident: CR2 article-title: Full discretization of semilinear stochastic wave equations driven by multiplicative noise publication-title: SIAM J. Numer. Anal. doi: 10.1137/15M101049X – volume: 14 start-page: 1 issue: 1 year: 2006 end-page: 12 ident: CR26 article-title: Midpoint rule for a linear stochastic oscillator with additive noise publication-title: Neural Parallel Sci. Comput. – volume: 78 start-page: 2047 issue: 268 year: 2009 end-page: 2074 ident: CR19 article-title: Conservative stochastic differential equations: Mathematical and numerical analysis publication-title: Math. Comp. doi: 10.1090/S0025-5718-09-02220-0 – volume: 357 start-page: 1021 issue: 1754 year: 1999 end-page: 1045 ident: CR33 article-title: Geometric integration using discrete gradients publication-title: R. Soc. Lond. Philos. Trans. Ser. A Math. Phys. Eng. Sci. doi: 10.1098/rsta.1999.0363 – volume: 54 start-page: 1993 issue: 3 year: 2016 end-page: 2013 ident: CR36 article-title: A characterization of energy-preserving methods and the construction of parallel integrators for Hamiltonian systems publication-title: SIAM J. Numer. Anal. doi: 10.1137/15M1020861 – volume: 51 start-page: 204 issue: 1 year: 2013 ident: 9771_CR14 publication-title: SIAM J. Numer Anal. doi: 10.1137/12087030X – ident: 9771_CR25 doi: 10.1007/3-540-45346-6_5 – volume: 13 start-page: 435 issue: 3 year: 2016 ident: 9771_CR8 publication-title: Int. J. Numer. Anal Model. – volume: 51 start-page: 699 issue: 44 year: 2004 ident: 9771_CR18 publication-title: BIT doi: 10.1007/s10543-004-5240-6 – ident: 9771_CR9 – volume: 54 start-page: 1093 issue: 2 year: 2016 ident: 9771_CR2 publication-title: SIAM J. Numer. Anal. doi: 10.1137/15M101049X – volume: 236 start-page: 3920 year: 2012 ident: 9771_CR6 publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2012.03.007 – volume-title: Numerical Solution of Stochastic Differential Equations, Volume 23 of Applications of Mathematics year: 1992 ident: 9771_CR30 doi: 10.1007/978-3-662-12616-5 – volume: 56 start-page: 1317 issue: 4 year: 2016 ident: 9771_CR31 publication-title: BIT doi: 10.1007/s10543-016-0608-y – volume: 49 start-page: 2017 issue: 5 year: 2011 ident: 9771_CR28 publication-title: SIAM J. Numer. Anal. doi: 10.1137/090771880 – ident: 9771_CR32 doi: 10.1007/978-3-319-33507-0_25 – volume: 83 start-page: 1689 issue: 288 year: 2014 ident: 9771_CR7 publication-title: Math. Comp. doi: 10.1090/S0025-5718-2014-02805-6 – volume: 82 start-page: 1478 issue: 8 year: 2012 ident: 9771_CR10 publication-title: Math. Comput. Simul. doi: 10.1016/j.matcom.2012.02.004 – volume: 56 start-page: 607 issue: 3 year: 2008 ident: 9771_CR20 publication-title: Oper. Res. doi: 10.1287/opre.1070.0496 – volume: 335 start-page: 51 year: 2018 ident: 9771_CR3 publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2017.11.043 – ident: 9771_CR16 doi: 10.1007/s10444-020-09771-5 – volume: 236 start-page: 3905 issue: 16 year: 2012 ident: 9771_CR4 publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2012.03.026 – volume: 14 start-page: 1 issue: 1 year: 2006 ident: 9771_CR26 publication-title: Neural Parallel Sci. Comput. – volume: 57 start-page: 123 issue: 1 year: 2017 ident: 9771_CR17 publication-title: BIT doi: 10.1007/s10543-016-0620-2 – volume: 56 start-page: 1497 issue: 4 year: 2016 ident: 9771_CR42 publication-title: BIT doi: 10.1007/s10543-016-0614-0 – volume-title: Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations, 2nd edn, Volume 31 of Springer Series in Computational Mathematics year: 2006 ident: 9771_CR23 – volume: 87 start-page: 38 year: 2015 ident: 9771_CR27 publication-title: Appl. Numer Math. doi: 10.1016/j.apnum.2014.08.003 – volume: 41 start-page: 045206, 7 issue: 4 year: 2008 ident: 9771_CR37 publication-title: J. Phys. A doi: 10.1088/1751-8113/41/4/045206 – volume: 54 start-page: 777 issue: 3 year: 2014 ident: 9771_CR35 publication-title: BIT doi: 10.1007/s10543-014-0474-4 – volume: 5 start-page: 73 issue: 1-2 year: 2010 ident: 9771_CR22 publication-title: J. Numer. Anal. Ind. Appl. Math. – volume: 1 start-page: 353 issue: 2 year: 2008 ident: 9771_CR38 publication-title: Discrete Contin. Dyn. Syst. Ser. S – volume: 346 start-page: 575 year: 2019 ident: 9771_CR24 publication-title: Appl. Math. Comput. doi: 10.1016/j.cam.2018.07.006 – volume: 121 start-page: 1 issue: 1 year: 2012 ident: 9771_CR15 publication-title: Numer. Math. doi: 10.1007/s00211-011-0426-8 – volume: 36 start-page: 276 issue: 2 year: 2018 ident: 9771_CR1 publication-title: J. Comput. Math. doi: 10.4208/jcm.1701-m2016-0525 – volume: 12 start-page: 1523 issue: 8 year: 2014 ident: 9771_CR12 publication-title: Commun. Math Sci. doi: 10.4310/CMS.2014.v12.n8.a7 – ident: 9771_CR11 doi: 10.1016/j.jcp.2020.109382 – volume: 235 start-page: 587 year: 2013 ident: 9771_CR41 publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2012.10.015 – volume: 51 start-page: 91 issue: 1 year: 2011 ident: 9771_CR13 publication-title: BIT doi: 10.1007/s10543-011-0310-z – volume: 6 start-page: 449 issue: 5 year: 1996 ident: 9771_CR21 publication-title: J. Nonlinear Sci. doi: 10.1007/BF02440162 – volume-title: Stochastic Numerics for Mathematical Physics. Scientific Computation year: 2004 ident: 9771_CR34 doi: 10.1007/978-3-662-10063-9 – volume: 55 start-page: 515 issue: 2 year: 2015 ident: 9771_CR39 publication-title: BIT doi: 10.1007/s10543-014-0507-z – volume: 51 start-page: 89 issue: 1 year: 2004 ident: 9771_CR40 publication-title: Appl. Numer. Math. doi: 10.1016/j.apnum.2004.02.003 – volume: 78 start-page: 2047 issue: 268 year: 2009 ident: 9771_CR19 publication-title: Math. Comp. doi: 10.1090/S0025-5718-09-02220-0 – volume: 65 start-page: 519 issue: 3 year: 2014 ident: 9771_CR5 publication-title: Numer. Algor. doi: 10.1007/s11075-013-9796-6 – volume: 54 start-page: 1993 issue: 3 year: 2016 ident: 9771_CR36 publication-title: SIAM J. Numer. Anal. doi: 10.1137/15M1020861 – volume: 357 start-page: 1021 issue: 1754 year: 1999 ident: 9771_CR33 publication-title: R. Soc. Lond. Philos. Trans. Ser. A Math. Phys. Eng. Sci. doi: 10.1098/rsta.1999.0363 – volume: 4 start-page: 87 issue: 1-2 year: 2009 ident: 9771_CR29 publication-title: J. Numer. Anal. Ind. Appl Math. |
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| Snippet | The paper deals with numerical discretizations of separable nonlinear Hamiltonian systems with additive noise. For such problems, the expected value of the... |
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| SubjectTerms | Computational mathematics Computational Mathematics and Numerical Analysis Computational Science and Engineering convergence differential-equations discretization driven Energy Exact solutions Hamiltonian functions Integrators invariants Matematik Mathematical and Computational Biology Mathematical Modeling and Industrial Mathematics Mathematical sciences Mathematics Mathematics and Statistics Multilevel Monte Carlo Nonlinear systems Numerical schemes runge-kutta methods simulation stage Stochastic differential equations Stochastic Hamiltonian systems Strong convergence Trace formula Visualization wave-equations Weak Weak convergence |
| Title | Drift-preserving numerical integrators for stochastic Hamiltonian systems |
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