Increasing the efficiency of numerical methods for estimating the state of a partially observed system. High order methods for solving parabolic PDEs
Lead Research Organisation:
University of Oxford
Department Name: Mathematical Institute
Abstract
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People |
ORCID iD |
| Terry Lyons (Principal Investigator) |
Publications
Boutaib Y
(2014)
Dimension-free Euler estimates of rough differential equations
in Rev. Roumaine Math. Pures Appl.
Cass T
(2013)
On The Error Estimate for Cubature on Wiener Space
in Proceedings of the Edinburgh Mathematical Society
Cass T
(2013)
Integrability and tail estimates for Gaussian rough differential equations
in The Annals of Probability
Cass T
(2015)
Evolving communities with individual preferences
in Proceedings of the London Mathematical Society
Crisan D
(2015)
Kusuoka-Stroock gradient bounds for the solution of the filtering equation
in Journal of Functional Analysis
Crisan D
(2010)
Probabilistic methods for semilinear partial differential equations. Applications to finance
in ESAIM: Mathematical Modelling and Numerical Analysis
Gyurk G
(2013)
Extracting information from the signature of a financial data stream
in arXiv e-prints
Gyurkó L
(2010)
Mathematics in Finance
Hambly B
(2010)
Uniqueness for the signature of a path of bounded variation and the reduced path group
in Annals of Mathematics
Lee Wonjung
(2013)
The adaptive patched particle filter and its implementation
in arXiv e-prints
Levin Daniel
(2013)
Learning from the past, predicting the statistics for the future, learning an evolving system
in arXiv e-prints
Liang G
(2011)
Backward stochastic dynamics on a filtered probability space
in The Annals of Probability
Liang G.
(2010)
A Functional Approach to FBSDEs and Its Application in Optimal Portfolios
in arXiv e-prints
Litterer C
(2012)
High order recombination and an application to cubature on Wiener space
in The Annals of Applied Probability
LYONS T
(2015)
The theory of rough paths via one-forms and the extension of an argument of Schwartz to rough differential equations
in Journal of the Mathematical Society of Japan
Lyons T
(2013)
The partial sum process of orthogonal expansions as geometric rough process with Fourier series as an example-An improvement of Menshov-Rademacher theorem
in Journal of Functional Analysis
Lyons T
(2017)
Hyperbolic development and inversion of signature
in Journal of Functional Analysis
| Description | Mathematical tools for filtering, and the methods studied in this project are useful for monitoring and controlling many different types of systems. The mathematics is very central to many types of problem - from weather prediction to engineering. This research made a useful contribution to the overall challenges, and formed a foundation for future research of the PIs. |
| Exploitation Route | High order methodology is mathematically challenging but very powerful. It can permit efficient anlysis of smaller datasets than might otherwise be the case. |
| Sectors | Aerospace, Defence and Marine,Digital/Communication/Information Technologies (including Software),Energy,Financial Services, and Management Consultancy,Manufacturing, including Industrial Biotechology,Pharmaceuticals and Medical Biotechnology,Retail,Security and Diplomacy,Transport,Other |
| Description | Not directly, there is an useful paper which considers exemplar models and integrated the new theory with practical data analysis effectively. One hopes this will form a bridge to applications in due course. The methods did demonstrate orders of magnitude increase in quality of prediction, however they are intellectually challenging to implement and so the exemplar paper becomes important - but will probably require follow up to achieve a full transition into the wider community. However, indirectly it stimulated useful further research work on recombination and scenario management that potentially accelerates certain important cases of the simplex algorithm. |
| First Year Of Impact | 2011 |
| Sector | Aerospace, Defence and Marine,Digital/Communication/Information Technologies (including Software),Electronics,Energy,Financial Services, and Management Consultancy,Healthcare,Manufacturing, including Industrial Biotechology,Security and Diplomacy,Other |
| Impact Types | Cultural,Economic |
| Description | An international collaboration of leading early stage contibutors to BSDE and cubature |
| Organisation | Government of China |
| Country | China |
| Sector | Public |
| PI Contribution | The grant enabled the PI to invite a small group of the leading international early stage reseachers in numerical methods for cubature and BSDE to work together in Oxford and establish collaboration. One outcome is a manuscript in which each of the following Danyu Yang Arnaud Lionnet Lajos Gergely Gyurkó Weijun Xu Dejan Velu?cek Maria Tchernychova Mariko Arisawa Camilo Andrés García Trillos Paul-Eric Chaudru de Raynal has, in a single collaborative work, written a short account of a key recent area for innovation. All have written their parts and near final version exists and should soon be placed on the Arxiv. A small group of the leading international early stage reseachers in numerical methods for cubature and BSDE worked together in Oxford and established a collaboration. Danyu Yang, Arnaud Lionnet, - Lajos Gergely Gyurkó, Weijun Xu, Dejan Velu?cek, Maria Tchernychova, Mariko Arisawa, Camilo Andrés García Trillos, Paul-Eric Chaudru de Raynal - have in a single collaborative work, written an account of key recent developments. A complete version exists and should soon be placed on the Arxiv. |
| Start Year | 2013 |
| Description | An international collaboration of leading early stage contibutors to BSDE and cubature |
| Organisation | Lubiana S.A |
| Country | Poland |
| Sector | Private |
| PI Contribution | The grant enabled the PI to invite a small group of the leading international early stage reseachers in numerical methods for cubature and BSDE to work together in Oxford and establish collaboration. One outcome is a manuscript in which each of the following Danyu Yang Arnaud Lionnet Lajos Gergely Gyurkó Weijun Xu Dejan Velu?cek Maria Tchernychova Mariko Arisawa Camilo Andrés García Trillos Paul-Eric Chaudru de Raynal has, in a single collaborative work, written a short account of a key recent area for innovation. All have written their parts and near final version exists and should soon be placed on the Arxiv. A small group of the leading international early stage reseachers in numerical methods for cubature and BSDE worked together in Oxford and established a collaboration. Danyu Yang, Arnaud Lionnet, - Lajos Gergely Gyurkó, Weijun Xu, Dejan Velu?cek, Maria Tchernychova, Mariko Arisawa, Camilo Andrés García Trillos, Paul-Eric Chaudru de Raynal - have in a single collaborative work, written an account of key recent developments. A complete version exists and should soon be placed on the Arxiv. |
| Start Year | 2013 |
| Description | An international collaboration of leading early stage contibutors to BSDE and cubature |
| Organisation | University of Nice Sophia-Antipolis |
| Country | France |
| Sector | Academic/University |
| PI Contribution | The grant enabled the PI to invite a small group of the leading international early stage reseachers in numerical methods for cubature and BSDE to work together in Oxford and establish collaboration. One outcome is a manuscript in which each of the following Danyu Yang Arnaud Lionnet Lajos Gergely Gyurkó Weijun Xu Dejan Velu?cek Maria Tchernychova Mariko Arisawa Camilo Andrés García Trillos Paul-Eric Chaudru de Raynal has, in a single collaborative work, written a short account of a key recent area for innovation. All have written their parts and near final version exists and should soon be placed on the Arxiv. A small group of the leading international early stage reseachers in numerical methods for cubature and BSDE worked together in Oxford and established a collaboration. Danyu Yang, Arnaud Lionnet, - Lajos Gergely Gyurkó, Weijun Xu, Dejan Velu?cek, Maria Tchernychova, Mariko Arisawa, Camilo Andrés García Trillos, Paul-Eric Chaudru de Raynal - have in a single collaborative work, written an account of key recent developments. A complete version exists and should soon be placed on the Arxiv. |
| Start Year | 2013 |