Terry Lyons
British mathematician
Terry Lyons 's AcademicInfluence.com Rankings
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Mathematics
Terry Lyons 's Degrees
- PhD Mathematics University of Oxford
Why Is Terry Lyons Influential?
(Suggest an Edit or Addition)According to Wikipedia, Terence John Lyons FLSW is a British mathematician, specialising in stochastic analysis. Lyons, previously the Wallis Professor of Mathematics, is a fellow of St Anne's College, Oxford and a Faculty Fellow at The Alan Turing Institute. He was the director of the Oxford-Man Institute from 2011 to 2015 and the president of the London Mathematical Society from 2013 to 2015. His mathematical contributions have been to probability, harmonic analysis, the numerical analysis of stochastic differential equations, and quantitative finance. In particular he developed what is now known as the theory of rough paths. Together with Patrick Kidger he proved a universal approximation theorem for neural networks of arbitrary depth.
Terry Lyons 's Published Works
Published Works
- Di erential equations driven by rough signals (1998) (1001)
- System Control and Rough Paths (2003) (584)
- Differential equations driven by rough paths (2007) (505)
- Stochastic finance. an introduction in discrete time (2004) (472)
- Uncertain volatility and the risk-free synthesis of derivatives (1995) (352)
- DIFFERENTIAL EQUATIONS DRIVEN BY ROUGH SIGNALS (I): AN EXTENSION OF AN INEQUALITY OF L. C. YOUNG (1994) (231)
- Function theory, random paths and covering spaces (1984) (226)
- Cubature on Wiener space (2004) (209)
- Uniqueness for the signature of a path of bounded variation and the reduced path group (2005) (209)
- Neural Controlled Differential Equations for Irregular Time Series (2020) (206)
- Falling out of bed: a relatively benign occurrence. (1993) (181)
- Universal Approximation with Deep Narrow Networks (2019) (179)
- Variable Step Size Control in the Numerical Solution of Stochastic Differential Equations (1997) (170)
- A Simple Criterion for Transience of a Reversible Markov Chain (1983) (149)
- Random Generation of Stochastic Area Integrals (1994) (107)
- A particle approximation of the solution of the Kushner–Stratonovitch equation (1999) (105)
- Discrete Filtering Using Branching and Interacting Particle Systems (1998) (103)
- Rough paths, Signatures and the modelling of functions on streams (2014) (100)
- Convergence of a Branching Particle Method to the Solution of the Zakai Equation (1998) (96)
- Learning Spatial-Semantic Context with Fully Convolutional Recurrent Network for Online Handwritten Chinese Text Recognition (2016) (90)
- INTEGRABILITY AND TAIL ESTIMATES FOR GAUSSIAN ROUGH DIFFERENTIAL EQUATIONS (2011) (90)
- Learning from the past, predicting the statistics for the future, learning an evolving system (2013) (86)
- Decomposition of Dirichlet Processes and its Application (1994) (84)
- The Signature of a Rough Path: Uniqueness (2014) (84)
- Nonlinear filtering and measure-valued processes (1997) (82)
- An extension theorem to rough paths (2007) (80)
- Deep Signature Transforms (2019) (78)
- A signature-based machine learning model for distinguishing bipolar disorder and borderline personality disorder (2017) (75)
- Performance and safety of rooftop wind turbines: Use of CFD to gain insight into inflow conditions (2014) (73)
- Instability of the Liouville property for quasi-isometric Riemannian manifolds and reversible Markov chains (1987) (72)
- A crossing estimate for the canonical process on a Dirichlet space and tightness result (1988) (70)
- Winding of the plane Brownian motion (1984) (69)
- LÉVY AREA OF WIENER PROCESSES IN BANACH SPACES (2002) (68)
- Characteristic functions of measures on geometric rough paths (2013) (64)
- Random forest prediction of Alzheimer’s disease using pairwise selection from time series data (2018) (64)
- Physical Brownian motion in a magnetic field as a rough path (2013) (58)
- Minimal Entropy Approximations and Optimal Algorithms (2002) (57)
- Interacting particle systems approximations of the Kushner-Stratonovitch equation (1999) (57)
- NUMERICAL METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS (2004) (56)
- Signatory: differentiable computations of the signature and logsignature transforms, on both CPU and GPU (2020) (56)
- Finely holomorphic functions (1980) (54)
- On conditional diffusion processes (1990) (52)
- Neural Rough Differential Equations for Long Time Series (2020) (51)
- Estimation of Regional Evapotranspiration through Remote Sensing (1999) (49)
- THE DEVELOPMENT OF A DRIVING CYCLE FOR FUEL CONSUMPTION AND EMISSIONS EVALUATION (1986) (49)
- Extending the Wong-Zakai theorem to reversible Markov processes (2002) (48)
- Extracting information from the signature of a financial data stream (2013) (47)
- Neural SDEs as Infinite-Dimensional GANs (2021) (46)
- Leveraging the Path Signature for Skeleton-based Human Action Recognition (2017) (44)
- Stochastic area for Brownian motion on the Sierpinski gasket (1998) (44)
- The Signature-Based Model for Early Detection of Sepsis From Electronic Health Records in the Intensive Care Unit (2019) (40)
- Integrability of Functionals of Dirichlet Processes, Probabilistic Representations of Semigroups, and Estimates of Heat Kernels (1998) (39)
- Effect of sharp vegetation boundary on the convective atmospheric boundary layer (2002) (38)
- Efficient and Practical Implementations of Cubature on Wiener Space (2011) (38)
- The Alzheimer's Disease Prediction Of Longitudinal Evolution (TADPOLE) Challenge: Results after 1 Year Follow-up (2020) (37)
- Discretely sampled signals and the rough Hoff process (2013) (37)
- A feature set for streams and an application to high-frequency financial tick data (2014) (36)
- Backward stochastic dynamics on a filtered probability space (2009) (35)
- Learning stochastic differential equations using RNN with log signature features (2019) (34)
- A Data-Driven Market Simulator for Small Data Environments (2020) (34)
- The Best Harmonic Approximant to a Continuous Function (1984) (32)
- Using path signatures to predict a diagnosis of Alzheimer’s disease (2018) (32)
- Evolving communities with individual preferences (2013) (32)
- Inverting the signature of a path (2014) (30)
- Forecasting Australian wheat yields with a weighted rainfall index (1994) (29)
- Hyperbolic development and inversion of signature (2015) (29)
- Rooftop wind monitoring campaigns for small wind turbine applications: Effect of sampling rate and averaging period (2015) (28)
- Optimal Execution with Rough Path Signatures (2019) (28)
- Flow of diffeomorphisms induced by a geometric multiplicative functional (1998) (28)
- Bases for Positive Continuous Functions (1990) (27)
- Developing the Path Signature Methodology and its Application to Landmark-based Human Action Recognition (2017) (27)
- The Limits of Stochastic Integrals of Differential Forms (1999) (27)
- The geometry of the Brownian curve (1993) (26)
- On the Importance of the Levy Area for Studying the Limits of Functions of Converging Stochastic Processes. Application to Homogenization (2003) (26)
- A note on tightness of capacities associated with Dirichlet forms (1992) (26)
- Modelling the structural loading of a small wind turbine at a highly turbulent site via modifications to the Kaimal turbulence spectra (2017) (25)
- Conditional exponential moments for iterated wiener integrals (1999) (25)
- Lévy's area under conditioning (2006) (25)
- Rotation-free online handwritten character recognition using dyadic path signature features, hanging normalization, and deep neural network (2016) (24)
- Smoothness of Itô maps and diffusion processes on path spaces (I) (2006) (23)
- Expected signature of Brownian Motion up to the first exit time from a bounded domain (2011) (23)
- Stopping non-commutative processes (1986) (23)
- Flow Equations on Spaces of Rough Paths (1997) (22)
- Integrability Estimates for Gaussian Rough Differential Equations (2011) (22)
- An Optimal Polynomial Approximation of Brownian Motion (2019) (21)
- Neural Controlled Differential Equations for Online Prediction Tasks (2021) (21)
- Application of the Signature Method to Pattern Recognition in the CEQUEL Clinical Trial (2016) (20)
- "Hey, that's not an ODE": Faster ODE Adjoints with 12 Lines of Code (2020) (20)
- The Signature Kernel Is the Solution of a Goursat PDE (2020) (19)
- Convergence of non-symmetric dirichlet processes (1996) (19)
- The critical dimension at which quasi-every Brownian path is self-avoiding (1986) (18)
- Note on Convergence of Dirichlet Processes (1993) (18)
- Dimension-free Euler estimates of rough differential equations (2013) (18)
- Non-parametric Pricing and Hedging of Exotic Derivatives (2019) (18)
- Utilization of the Signature Method to Identify the Early Onset of Sepsis From Multivariate Physiological Time Series in Critical Care Monitoring (2020) (17)
- A Class of Vector Fields on Path Spaces (1997) (17)
- A Generalised Signature Method for Multivariate Time Series Feature Extraction (2021) (17)
- Detecting early signs of depressive and manic episodes in patients with bipolar disorder using the signature-based model (2017) (16)
- Diffusion processes with non-smooth diffusion coefficients and their density functions (1990) (16)
- Extent to which international wind turbine design standard, IEC61400-2 is valid for a rooftop wind installation (2015) (16)
- Analysis on Riemannian co-compact covers (2006) (15)
- A Path Signature Approach for Speech Emotion Recognition (2019) (15)
- Planning of bed capacities in specialized and integrated care units: Incorporating bed blockers in a simulation of surgical throughput (2012) (15)
- Areas of areas generate the shuffle algebra (2020) (15)
- Distribution Regression for Sequential Data (2020) (15)
- Numerical Simulation of a Sea Breeze Under Dominant Synoptic Conditions at Perth (2000) (14)
- Sound compression: a rough path approach (2005) (14)
- Stochastic Jacobi fields and vector fields induced by varying area on path spaces (1997) (13)
- Efficient and Accurate Gradients for Neural SDEs (2021) (13)
- A Generalised Signature Method for Time Series (2020) (13)
- Uniform Factorial Decay Estimates for Controlled Differential Equations (2015) (13)
- A synthetic proof of Makarov's law of the iterated logarithm (1990) (13)
- Rough Paths based Numerical Algorithms in Computational Finance (2008) (12)
- Jensen Measures for R(K) (1983) (12)
- Neural CDEs for Long Time Series via the Log-ODE Method (2020) (12)
- Instability of the conservative property under quasi-isometries (1991) (12)
- A signed measure on rough paths associated to a PDE of high order: results and conjectures (2009) (12)
- On the radius of convergence of the logarithmic signature (2006) (11)
- On Gauss–Green theorem and boundaries of a class of Hölder domains (2006) (11)
- Mesoscale wind spectra (1975) (11)
- A Path Signature Approach to Online Arabic Handwriting Recognition (2018) (11)
- Rough Paths on Manifolds (2011) (11)
- Pathwise approximation of SDEs by coupling piecewise abelian rough paths (2015) (11)
- SigGPDE: Scaling Sparse Gaussian Processes on Sequential Data (2021) (11)
- A theorem in fine potential theory and applications to finely holomorphic functions (1980) (11)
- Projection theorems for hitting probabilities and a theorem of Littlewood (1984) (10)
- DIRICHLET FORMS AND SYMMETRIC MARKOV PROCESSES (Studies in Mathematics 19) By Masatoshi Fukushima, Yoshida Oshima and Masayoshi Takeda: 392 pp., DM.168.–/US$79–95, ISBN 3 11 011626 X (Walter de Gruyter, 1994). (1997) (10)
- SK-Tree: a systematic malware detection algorithm on streaming trees via the signature kernel (2021) (9)
- Cones of lower semicontinuous functions and a characterisation of finely hyperharmonic functions (1982) (9)
- The shifted ODE method for underdamped Langevin MCMC (2021) (9)
- "Hey, that's not an ODE": Faster ODE Adjoints via Seminorms (2020) (9)
- Higher Order Kernel Mean Embeddings to Capture Filtrations of Stochastic Processes (2021) (9)
- Integration of time-varying cocyclic one-forms against rough paths (2014) (8)
- Generating Financial Markets With Signatures (2020) (8)
- Positively Weighted Kernel Quadrature via Subsampling (2021) (8)
- Some notes on trees and paths (2008) (8)
- The theory of rough paths via one-forms and the extension of an argument of Schwartz to rough differential equations (2015) (8)
- Uniqueness for the signature of a path of bounded variation and continuous analogues of the free group (2005) (8)
- Learning to Detect Bipolar Disorder and Borderline Personality Disorder with Language and Speech in Non-Clinical Interviews (2020) (8)
- Finely Harmonic Functions need not be Quasi-Analytic (1984) (8)
- The partial sum process of orthogonal expansions as geometric rough process with Fourier series as an example—An improvement of Menshov–Rademacher theorem (2011) (8)
- Signature Methods in Machine Learning (2022) (7)
- Generalised Interpretable Shapelets for Irregular Time Series (2020) (7)
- Cubature on Wiener Space Continued (2007) (7)
- Systems Controlled by Rough Paths (2005) (6)
- Expected signature of two dimensional Brownian Motion up to the first exit time of the domain (2011) (6)
- Super-multiplicativity and a lower bound for the decay of the signature of a path of finite length (2018) (5)
- Estimating the probability that a given vector is in the convex hull of a random sample (2021) (5)
- Note on the Signatures of Rough Paths in a Banach Space (2015) (5)
- Inversion of signature for paths of bounded variation (2011) (5)
- Numerical Methods and Stochastics (2002) (5)
- A new definition of rough paths on manifolds (2015) (5)
- An Asymptotic Radius of Convergence for the Loewner Equation and Simulation of $$SLE_{\kappa }$$ Traces via Splitting (2019) (5)
- Rough Path Analysis (5)
- Computing the full signature kernel as the solution of a Goursat problem (2020) (4)
- Insertion algorithm for inverting the signature of a path (2019) (4)
- Anomaly detection on streamed data (2020) (4)
- Numerical Method for Model-free Pricing of Exotic Derivatives in Discrete Time Using Rough Path Signatures (2019) (4)
- Smooth rough paths and applications to Fourier analysis (2007) (4)
- A uniform estimate for rough paths (2011) (4)
- Sketching the order of events (2017) (4)
- Numerical method for model-free pricing of exotic derivatives using rough path signatures (2019) (4)
- Continuity in κ in SLEκ theory using a constructive method and Rough Path Theory (2021) (4)
- Model-free pricing and hedging in discrete time using rough path signatures (2019) (4)
- Distribution Regression for Continuous-Time Processes via the Expected Signature (2020) (4)
- Comments on ‘Canyon geometry and the nocturnal urban Heat Island: Comparisons of scale model and field observations’ (1983) (4)
- Kusuoka-Stroock gradient bounds for the solution of the filtering equation (2013) (4)
- An application of fine potential theory to prove a Phragmen Lindelöf theorem (1984) (3)
- Survey Lecturers (2008) (3)
- Neural SDEs Made Easy: SDEs are Infinite-Dimensional GANS (2020) (3)
- On boundary conditions for stochastic evolution equations with an extremally chaotic source (1995) (3)
- Computing the untruncated signature kernel as the solution of a Goursat problem (2020) (3)
- Rough differential equation in Banach space driven by weak geometric p-rough path (2014) (3)
- A Functional Approach to FBSDEs and Its Application in Optimal Portfolios (2010) (3)
- A new approach to SLE phase transition (2020) (3)
- The theory of rough paths via one-forms and the extension of an argument of Schwartz to RDEs (2015) (2)
- Recovering the pathwise Itô solution from averaged Stratonovich solutions (2016) (2)
- On Ito differential equation in rough path theory (2013) (2)
- Logsig-RNN: a novel network for robust and efficient skeleton-based action recognition (2021) (2)
- The adaptive patched cubature filter and its implementation (2015) (2)
- Modelling Paralinguistic Properties in Conversational Speech to Detect Bipolar Disorder and Borderline Personality Disorder (2021) (2)
- A Definition of BMO p for an Abstract Harmonic Space and a John-Nirenberg Theorem (1980) (2)
- Deep Signatures (2019) (1)
- Information Extraction from Swedish Medical Prescriptions with Sig-Transformer Encoder (2020) (1)
- The adaptive patched particle filter and its implementation (2013) (1)
- Uniform Factorial Decay Estimate for the Remainder of Rough Taylor Expansion (2015) (1)
- General Signature Kernels (2021) (1)
- Deriving information from missing data: implications for mood prediction (2020) (1)
- Corrigendum to “Super-multiplicativity and a lower bound for the decay of the signature of a path of finite length” [C. R. Acad. Sci. Paris, Ser. I 356 (7) (2018) 720–724] (2018) (1)
- Labelling as an unsupervised learning problem (2018) (1)
- Convergence to closed-form distribution for the backward $SLE_κ$ at some random times and the phase transition at $κ=8$ (2019) (1)
- Dual Bayesian ResNet: A Deep Learning Approach to Heart Murmur Detection (2022) (1)
- ImageSig: A signature transform for ultra-lightweight image recognition (2022) (1)
- Discretely sampled signals and the rough Hoff path (2013) (1)
- A Feature Set for Streams and a Demonstration on High-Frequency Financial Tick Data (2014) (1)
- BROWNIAN ROUGH PATHS (2002) (1)
- Smooth Rough Paths and the Applications (2007) (1)
- Sampling-based Nyström Approximation and Kernel Quadrature (2023) (1)
- Finely Open Sets in the Limit Set of a Finitely Generated Kleinian Group (1992) (1)
- The insertion method to invert the signature of a path (2023) (0)
- K. Itô Introduction to probability theory (Cambridge University Press, 1984), 211 pp. £18.50 cloth,£6.95 paper. (1985) (0)
- A Personal Perspective on Raghu Varadhan’s Role in the Development of Stochastic Analysis (2010) (0)
- PATH INTEGRATION ALONG ROUGH PATHS (2002) (0)
- 2022 Half shuffle identities in arity 3 on Zinbiel and Tortkara algebras and a structure theorem for streamed information (2022) (0)
- On Exponential Bounds for Solutions of Second order Differential Equations (1985) (0)
- S IGNATORY : DIFFERENTIABLE COMPUTATIONS OF THE SIGNATURE AND LOGSIGNATURE TRANSFORMS , ON BOTH CPU AND GPU (2021) (0)
- An Optimal Polynomial Approximation of Brownian Motion | SIAM Journal on Numerical Analysis | Vol. 58, No. 3 | Society for Industrial and Applied Mathematics (2020) (0)
- Optimal Stopping via Distribution Regression: a Higher Rank Signature Approach (2023) (0)
- Identifying psychiatric diagnosis from missing mood data through the use of log-signature features (2022) (0)
- Path Signatures for Non-Intrusive Load Monitoring (2022) (0)
- Convergence to Closed-Form Distribution for the Backward $Sle_{\Kappa}$ at Some Random Times and the Phase Transition at $\Kappa=8$ (2019) (0)
- TITLES AND ABSTRACTS (2022) (0)
- LOG-ODE METHOD (2020) (0)
- Optimal Execution with Rough Path (2020) (0)
- Partial sum process of orthogonal series as rough process (2012) (0)
- Order book models, signatures and numerical approximations of rough differential equations (2012) (0)
- Making high order methods effective (2016) (0)
- New directions in the applications of rough path theory (2023) (0)
- A structure theorem for streamed information (2022) (0)
- UNIVERSAL LIMIT THEOREM (2002) (0)
- Continuity in $\kappa$ in $SLE_\kappa$ theory using a constructive method and Rough Path Theory (2020) (0)
- Benchmarking optimality of time series classification methods in distinguishing diffusions (2023) (0)
- C A ] 1 5 O ct 2 01 5 The Signature of a Rough Path : Uniqueness (2018) (0)
- Hypercontractivity Meets Random Convex Hulls: Analysis of Randomized Multivariate Cubatures (2022) (0)
- Generalised Recombination Interpolation Method (GRIM) (2022) (0)
- Learning Dynamic Graph Embeddings with Neural Controlled Differential Equations (2023) (0)
- Numerical methods for approximating solutions to rough differential equations (2008) (0)
- Martingale decomposition of Dirichlet processes on the Banach space C0[0, 1] (1996) (0)
- VECTOR FIELDS AND FLOW EQUATIONS (2002) (0)
- Counseling and Life-Span Development, R. Thomas. From Sage Publications, Inc., 2111 West Hill Crest Drive, Newbury Park, CA 91320 (1989), 367 pp., softcover, $18.95., ISBN: 0-8039-3614-1 (1991) (0)
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