--- references: - id: BeckMachine2019 accessed: - year: 2020 month: 9 day: 16 author: - family: Beck given: Christian - family: E given: Weinan - family: Jentzen given: Arnulf citation-key: BeckMachine2019 container-title: Journal of Nonlinear Science container-title-short: J Nonlinear Sci DOI: 10.1007/s00332-018-9525-3 ISSN: 0938-8974, 1432-1467 issue: '4' issued: - year: 2019 month: 8 language: en page: 1563-1619 title: >- Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations type: article-journal URL: http://arxiv.org/abs/1709.05963 volume: '29' - id: CerouSequential2011 accessed: - year: 2015 month: 2 day: 11 author: - family: Cérou given: F. - family: Moral given: P. Del - family: Furon given: T. - family: Guyader given: A. citation-key: CerouSequential2011 container-title: Statistics and Computing container-title-short: Stat Comput DOI: 10.1007/s11222-011-9231-6 ISSN: 0960-3174, 1573-1375 issue: '3' issued: - year: 2011 month: 4 day: 5 language: en page: 795-808 title: Sequential Monte Carlo for rare event estimation type: article-journal URL: https://hal.inria.fr/inria-00584352 volume: '22' - id: ChanWaiNamMachine2019 accessed: - year: 2023 month: 3 day: 3 author: - family: Chan-Wai-Nam given: Quentin - family: Mikael given: Joseph - family: Warin given: Xavier citation-key: ChanWaiNamMachine2019 container-title: Journal of Scientific Computing container-title-short: J Sci Comput DOI: 10.1007/s10915-019-00908-3 ISSN: 1573-7691 issue: '3' issued: - year: 2019 month: 6 day: 1 language: en page: 1667-1712 title: Machine Learning for Semi Linear PDEs type: article-journal URL: http://arxiv.org/abs/1809.07609 volume: '79' - id: ChopinIntroduction2020 accessed: - year: 2020 month: 10 day: 8 author: - family: Chopin given: Nicolas - family: Papaspiliopoulos given: Omiros citation-key: ChopinIntroduction2020 collection-title: Springer Series in Statistics DOI: 10.1007/978-3-030-47845-2 ISBN: 978-3-030-47844-5 issued: - year: 2020 language: en publisher: Springer International Publishing title: An Introduction to Sequential Monte Carlo type: book URL: https://www.springer.com/gp/book/9783030478445 - id: ChuangFeynmanKac2010 accessed: - year: 2021 month: 1 day: 26 author: - family: Chuang given: Howard Jen-Hao citation-key: ChuangFeynmanKac2010 genre: Honours issued: - year: 2010 publisher: ANU title: >- The Feynman-Kac Formula:Relationships Between Stochastic DifferentialEquations and Partial Differential Equations type: thesis URL: >- https://maths-intranet.anu.edu.au/MSIonly/honours_theses/2010/Howard_Chuang.pdf - id: DelMoralBranching2000 accessed: - year: 2014 month: 8 day: 27 author: - family: Del Moral given: Pierre - family: Miclo given: Laurent citation-key: DelMoralBranching2000 collection-number: '1729' collection-title: Lecture Notes in Mathematics container-title: Séminaire de Probabilités XXXIV DOI: 10.1007/BFb0103798 ISBN: 978-3-540-67314-9 978-3-540-46413-6 issued: - year: 2000 language: en page: 1–145 publisher: Springer title: >- Branching and interacting particle systems approximations of Feynman-Kac formulae with applications to non-linear filtering type: chapter URL: http://perso.math.univ-toulouse.fr/miclo/files/2012/04/branching.pdf - id: DelMoralConcentration2011 accessed: - year: 2014 month: 8 day: 27 author: - family: Del Moral given: Pierre - family: Hu given: Peng - family: Wu given: Liming citation-key: DelMoralConcentration2011 DOI: 10.1561/2200000026 issued: - year: 2011 month: 7 day: 11 language: en publisher: Now Publishers title: On the concentration properties of Interacting particle processes type: book URL: http://arxiv.org/abs/1107.1948 volume: '3' - id: DelMoralFeynmanKac2004 author: - family: Del Moral given: Pierre citation-key: DelMoralFeynmanKac2004 edition: 2004 edition event-place: Latheronwheel, Caithness ISBN: 978-1-870325-07-3 issued: - year: 2004 month: 3 day: 30 language: English number-of-pages: '580' publisher: Springer publisher-place: Latheronwheel, Caithness title: >- Feynman-Kac Formulae: Genealogical and Interacting Particle Systems with Applications type: book - id: DelMoralInteracting2010 accessed: - year: 2014 month: 8 day: 27 author: - family: Del Moral given: Pierre - family: Doucet given: Arnaud citation-key: DelMoralInteracting2010 container-title: The Annals of Applied Probability container-title-short: Ann. Appl. Probab. DOI: 10.1214/09-AAP628 ISSN: 1050-5164, 2168-8737 issue: '2' issued: - year: 2010 month: 4 language: EN page: 593-639 title: >- Interacting Markov chain Monte Carlo methods for solving nonlinear measure-valued equations type: article-journal volume: '20' - id: DoucetSequential2000 accessed: - year: 2017 month: 11 day: 14 author: - family: Doucet given: Arnaud - family: Godsill given: Simon - family: Andrieu given: Christophe citation-key: DoucetSequential2000 container-title: Statistics and Computing container-title-short: Statistics and Computing DOI: 10.1023/A:1008935410038 ISSN: 0960-3174, 1573-1375 issue: '3' issued: - year: 2000 month: 7 day: 1 language: en number: '3' page: 197-208 title: On sequential Monte Carlo sampling methods for Bayesian filtering type: article-journal volume: '10' - id: DoucetSequential2001 accessed: - year: 2017 month: 9 day: 1 author: - family: Doucet given: Arnaud - family: Freitas given: Nando - family: Gordon given: Neil citation-key: DoucetSequential2001 event-place: New York, NY ISBN: 978-1-4757-3437-9 issued: - year: 2001 language: English publisher: Springer New York publisher-place: New York, NY title: Sequential Monte Carlo Methods in Practice type: book URL: http://public.eblib.com/choice/publicfullrecord.aspx?p=3087052 - id: EDeep2017 accessed: - year: 2022 month: 7 day: 19 author: - family: E given: Weinan - family: Han given: Jiequn - family: Jentzen given: Arnulf citation-key: EDeep2017 container-title: Communications in Mathematics and Statistics container-title-short: Commun. Math. Stat. DOI: 10.1007/s40304-017-0117-6 ISSN: 2194-671X issue: '4' issued: - year: 2017 month: 12 day: 1 language: en page: 349-380 title: >- Deep Learning-Based Numerical Methods for High-Dimensional Parabolic Partial Differential Equations and Backward Stochastic Differential Equations type: article-journal URL: http://arxiv.org/abs/1706.04702 volume: '5' - id: HanSolving2018 accessed: - year: 2019 month: 8 day: 27 author: - family: Han given: Jiequn - family: Jentzen given: Arnulf - family: E given: Weinan citation-key: HanSolving2018 container-title: Proceedings of the National Academy of Sciences container-title-short: PNAS DOI: 10.1073/pnas.1718942115 ISSN: 0027-8424, 1091-6490 issue: '34' issued: - year: 2018 month: 8 day: 21 language: en page: 8505-8510 PMCID: PMC6112690 PMID: '30082389' publisher: National Academy of Sciences section: Physical Sciences title: Solving high-dimensional partial differential equations using deep learning type: article-journal volume: '115' - id: HartmannVariational2017 accessed: - year: 2023 month: 3 day: 3 author: - family: Hartmann given: Carsten - family: Richter given: Lorenz - family: Schütte given: Christof - family: Zhang given: Wei citation-key: HartmannVariational2017 container-title: Entropy DOI: 10.3390/e19110626 ISSN: 1099-4300 issue: '11' issued: - year: 2017 month: 11 language: en number: '11' page: '626' publisher: Multidisciplinary Digital Publishing Institute title: 'Variational Characterization of Free Energy: Theory and Algorithms' type: article-journal URL: https://www.mdpi.com/1099-4300/19/11/626 volume: '19' - id: HutzenthalerMultilevel2020 accessed: - year: 2023 month: 3 day: 3 author: - family: Hutzenthaler given: Martin - family: Kruse given: Thomas citation-key: HutzenthalerMultilevel2020 container-title: SIAM Journal on Numerical Analysis container-title-short: SIAM J. Numer. Anal. DOI: 10.1137/17M1157015 ISSN: 0036-1429 issue: '2' issued: - year: 2020 month: 1 page: 929-961 publisher: Society for Industrial and Applied Mathematics title: >- Multilevel Picard Approximations of High-Dimensional Semilinear Parabolic Differential Equations with Gradient-Dependent Nonlinearities type: article-journal URL: http://arxiv.org/abs/1711.01080 volume: '58' - id: HutzenthalerOvercoming2020 accessed: - year: 2023 month: 3 day: 3 author: - family: Hutzenthaler given: Martin - family: Jentzen given: Arnulf - family: Kruse given: Thomas - family: Anh Nguyen given: Tuan - family: Wurstemberger given: Philippe non-dropping-particle: von citation-key: HutzenthalerOvercoming2020 container-title: >- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences DOI: 10.1098/rspa.2019.0630 issue: '2244' issued: - year: 2020 month: 12 day: 16 page: '20190630' publisher: Royal Society title: >- Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations type: article-journal URL: http://arxiv.org/abs/1807.01212 volume: '476' - id: KebiriAdaptive2019 author: - family: Kebiri given: Omar - family: Neureither given: Lara - family: Hartmann given: Carsten citation-key: KebiriAdaptive2019 collection-title: Springer Proceedings in Mathematics & Statistics container-title: Stochastic Dynamics Out of Equilibrium DOI: 10.1007/978-3-030-15096-9_7 editor: - family: Giacomin given: Giambattista - family: Olla given: Stefano - family: Saada given: Ellen - family: Spohn given: Herbert - family: Stoltz given: Gabriel event-place: Cham ISBN: 978-3-030-15096-9 issued: - year: 2019 language: en page: 265-281 publisher: Springer International Publishing publisher-place: Cham title: >- Adaptive Importance Sampling with Forward-Backward Stochastic Differential Equations type: paper-conference URL: http://arxiv.org/abs/1802.04981 - id: NualartBackward2001 accessed: - year: 2021 month: 1 day: 26 author: - family: Nualart given: David - family: Schoutens given: Wim citation-key: NualartBackward2001 container-title: Bernoulli container-title-short: Bernoulli ISSN: 1350-7265 issue: '5' issued: - year: 2001 month: 10 language: EN page: 761-776 publisher: Bernoulli Society for Mathematical Statistics and Probability title: >- Backward stochastic differential equations and Feynman-Kac formula for Lévy processes, with applications in finance type: article-journal URL: https://projecteuclid.org/euclid.bj/1079399541 volume: '7' - id: NuskenSolving2021 accessed: - year: 2023 month: 3 day: 3 author: - family: Nüsken given: Nikolas - family: Richter given: Lorenz citation-key: NuskenSolving2021 container-title: Partial Differential Equations and Applications container-title-short: Partial Differ. Equ. Appl. DOI: 10.1007/s42985-021-00102-x ISSN: 2662-2971 issue: '4' issued: - year: 2021 month: 6 day: 21 language: en page: '48' title: >- Solving high-dimensional Hamilton–Jacobi–Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path space type: article-journal URL: http://arxiv.org/abs/2005.05409 volume: '2' - id: PapanicolaouIntroduction2019 accessed: - year: 2021 month: 1 day: 13 author: - family: Papanicolaou given: Andrew citation-key: PapanicolaouIntroduction2019 container-title: arXiv:1504.05309 [math, q-fin] issued: - year: 2019 month: 1 day: 2 title: Introduction to Stochastic Differential Equations (SDEs) for Finance type: article-journal URL: http://arxiv.org/abs/1504.05309 ...