Di erential equations driven by rough signals
- Terry Lyons
- Mathematics
- 31 August 1998
This paper aims to provide a systematic approach to the treatment of differential equations of the type
dyt = Si fi(yt) dxti
where the driving signal xt is a rough path. Such equations are very…
Stochastic finance. an introduction in discrete time
- Terry Lyons
- Economics
- 1 September 2004
System Control and Rough Paths
- Terry Lyons, Z. Qian
- Mathematics
- 6 February 2003
0. Preface 1. Introduction 2. Lipschitz paths 3. Rough paths 4. Brownian rough paths 5. Path integration along rough paths 6. Universal limit theoem 7. Vector fields and Flow Equations
Differential equations driven by rough paths
- Terry Lyons, M. Caruana, Thierry Lévy, École d'été de probabilités de Saint-Flour
- Mathematics, Geology
- 2007
Differential Equations Driven by Moderately Irregular Signals.- The Signature of a Path.- Rough Paths.- Integration Along Rough Paths.- Differential Equations Driven by Rough Paths.
Neural Controlled Differential Equations for Irregular Time Series
- Patrick Kidger, James Morrill, James Foster, Terry Lyons
- Computer ScienceNeural Information Processing Systems
- 18 May 2020
The resultingural controlled differential equation model is directly applicable to the general setting of partially-observed irregularly-sampled multivariate time series, and (unlike previous work on this problem) it may utilise memory-efficient adjoint-based backpropagation even across observations.
Uncertain volatility and the risk-free synthesis of derivatives
- Terry Lyons
- Mathematics
- 1 June 1995
To price contingent claims in a multidimensional frictionless security market it is sufficient that the volatility of the security process is a known function of price and time. In this note we…
Uniqueness for the signature of a path of bounded variation and the reduced path group
- B. Hambly, Terry Lyons
- Mathematics
- 26 July 2005
We introduce the notions of tree-like path and tree-like equivalence between paths and prove that the latter is an equivalence relation for paths of finite length. We show that the equivalence…
Cubature on Wiener space
- Terry Lyons, Nicolas Victoir
- Mathematics, Computer ScienceProceedings of the Royal Society of London…
- 8 January 2004
This work discusses the appropriate extension of cubature to Wiener space and develops high–order numerical schemes valid for high–dimensional SDEs and semi–elliptic PDEs.
Variable Step Size Control in the Numerical Solution of Stochastic Differential Equations
- J. Gaines, Terry Lyons
- MathematicsSIAM Journal on Applied Mathematics
- 1 October 1997
A variable step size method for the numerical approximation of pathwise solutions to stochastic differential equations (SDEs) and its dependence on a representation of Bro...
DIFFERENTIAL EQUATIONS DRIVEN BY ROUGH SIGNALS (I): AN EXTENSION OF AN INEQUALITY OF L. C. YOUNG
- Terry Lyons
- Mathematics
- 1994
If one fixes x one may ask about the existence and uniqueness of y with finite p-variation where to avoid triviality we assume d > 1. We prove that if each f i is (1+α)-Lipschitz in the sense of [7]…
...
...