EPSRC Reference: 
EP/M00516X/1 
Title: 
Constrained random phenomena using rough paths 
Principal Investigator: 
Cass, Professor T 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Mathematics 
Organisation: 
Imperial College London 
Scheme: 
First Grant  Revised 2009 
Starts: 
01 October 2014 
Ends: 
30 September 2016 
Value (£): 
87,527

EPSRC Research Topic Classifications: 

EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


Related Grants: 

Panel History: 
Panel Date  Panel Name  Outcome 
10 Sep 2014

EPSRC Mathematics Prioritisation Panel Sept 2014

Announced


Summary on Grant Application Form 
Random process are ubiquitous throughout the natural and manmade world. These processes are often observed, measured or experienced as paths evolving over time in some state space. The effect of noise often makes the trajectory of these evolving paths unpredictable and highly erratic. In simple examples, such as the movement of a share price, the state space might be the nonnegative real numbers. In more general examples the dynamics of the evolution may be constrained, such as the movement of a rigid body, or the evolution of particles in a section of the earth's atmosphere. This project will develop broad modelling framework for the analysis of highlyenergetic random trajectories on curved spaces. A key ingredient of this will be the use Lyons' rough path analysis.
The precise study of Brownian motion over the last century has led to spectacular results in the modelling of natural phenomena. Our understanding of manifoldvalued Brownian motion was given great impetus by the EellsElworthyMalliavin global construction of Riemannian Brownian motion. It is now however increasingly well understood that model based on Brownian motion are not always appropriate; persistence, longtime dependence and momentum are longobserved features of behaviour in queueing networks for internettraffic, in hydrology, and in the fluctuation of market prices. Brownian motion belongs to a fundamental class of random processes in statistics called Gaussian processes. This class is both simple enough to work with, and broad enough to capture random memoryeffects in evolving systems.
In this project will will combine techniques from stochastic analysis, probability the theory of rough paths and stochastic differential geometry to study, in a precise and quantitative way, properties of a class of Gaussian processes on Riemannian manifolds. We expect there to be interesting interplay between the randomness and the geometry of the space which the process inhabits. A key objective of the project will be to furnish the wider scientific community with deeper understanding and techniques which they can utilise in their work.

Key Findings 
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Potential use in nonacademic contexts 
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Impacts 
Description 
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Summary 

Date Materialised 


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Project URL: 

Further Information: 

Organisation Website: 
http://www.imperial.ac.uk 