Cónall Kelly
Lecturer Department of Mathematics and Computer Science, University of the West Indies. Room 4, External phone number: +876 977 2693 Extension: 2284/2455 Intercom: 234 Email: conall
“dot” kelly “at” uwimona “dot”
edu “dot” jm Research
I am
interested the way that imperfect feedback influences the behaviour of
dynamical systems. Noise and
delay can cause a system to oscillate. Noise can also affect the stability of
a system – appropriately structured random perturbations can act to either
stabilise or destabilise a system of differential equations. In fact, a noise
perturbation can act to suppress the occurrence of an explosion in a system. Stochastic functional differential equations, the mathematical
representation of such systems, find applications in many areas. For example,
population dynamics are influenced not only by delay (gestation and maturation
periods), but also by noise (disease, weather, and other random environmental
factors). Other applications include neural network models and finance. We draw
on theoretical techniques from stochastic and deterministic analysis, but
also use dynamically consistent discrete-time models to capture the essential
behaviour of a stochastic process. Often these models are more amenable to
analysis than the original process in continuous time. An offshoot of this
approach is that numerical simulation plays an important role in developing
our intuition. Academic History
My PhD thesis, submitted to Dublin City University
in July 2005, is entitled ‘On the Oscillatory Behaviour of Stochastic Delay Equations’
and you can download it here. From August 2005 until August 2006 I held a postdoctoral
position at University
College Cork, working with the Probability
Group, headed by Prof. Neil O’Connell. The Probability Group, supported by
SFI grant 04/RP1/L512 “Probability and its applications”, was part of the School of
Mathematical Sciences and the Boole Centre for
Research in Informatics. Since August 2006 I have been a lecturer in the Department
of Mathematics and Computer Science at the University of the
West Indies, Teaching
(2007/08)
Semester
1: M25A - Probability Theory. Semester
2: M25B - Statistical Inference. M33R - Complex Analysis. Teaching materials for courses currently in session can be found
on OurVLE – the university’s online learning system, accessible to students here. Seminar Series
I co-ordinate the regular
research seminar held in the Mathematics Lecture
Theatre on Fridays at 11am during term.
Publications
(preprints and offprints available on request)
John A.D. Appleby, Cónall Kelly, and Alexandra Rodkina. Dynamical consistency of solutions of continuous and discrete
stochastic equations with a finite time explosion. Proceedings
of the Twelfth International
Conference on Difference Equations and Applications. Submitted. John A.D. Appleby, Xuerong Mao, Cónall Kelly, and Alexandra
Rodkina. Positivity and Stabilization for Nonlinear Stochastic Delay
Differential Equations. Stochastics: An International
Journal of Probability and Stochastic Processes.
Submitted. John A.D. Appleby and Cónall Kelly. Spurious oscillation in a uniform Euler discretisation of linear
stochastic differential equations with vanishing delay. J. Comput. Appl. Math. 205 (2007), no. 2,
923-925. John A.D. Appleby and Cónall Kelly. Almost Sure Asymptotic Behaviour of One- and Two-step Difference
Equations with Random Coefficients on a Reducing Mesh. Proceedings of the IX International Chetayev Conference: Analytical Mechanics, Stability and
Control of Motion, (2007). John A.D. Appleby and Cónall Kelly. Oscillation of solutions of a nonuniform discretisation of
linear stochastic differential equations with vanishing delay. Dyn.
Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 13B
(2006), suppl., 535-550. John
A. D. Appleby and Cónall Kelly. Prevention of Explosions in Solutions of Functional Differential
Equations by Noise Perturbation. Dynamic
Systems and Applications, 15 (2006), no. 2, 227–240. John
A. D. Appleby and Cónall Kelly. Asymptotic and Oscillatory Properties of Linear Stochastic Delay
Differential Equations with Vanishing Delay. Functional
Differential Equations, 11
(2004), no. 3–4, 235–265. John
A. D. Appleby and Cónall Kelly. Oscillation and Non-oscillation in Solutions of Nonlinear
Stochastic Delay Differential Equations. Electronic
Communications in Probability, 9 (2004), 106–118. Presentations
2006/07
Stabilisation
and Destabilisation by Noise. UWI
Mathematics Seminar, 28 September 2007, University of
the West Indies, Explosions
in Discrete Time. DCU
Mathematics Seminar, 3 August 2007, Dynamical
Consistency in Discrete and Continuous Equations with Finite-Time Explosions. 12th
International Conference on Difference Equations and Applications, 26 July 2007, Instituto Superior Tecnico,
Technical Consistency
in the Oscillatory Dynamics of Discrete and Continuous Stochastic Equations. IX
International Chetayev Conference: Analytical
Mechanics, Stability and Control of Motion, 13 June 2007, The
Institute for System Dynamics and Control Theory, Siberian Branch, Russian
Academy of Sciences, Irkutsk, Russian Federation. Nonlinear
Stochastic Functional Differential Equations: Stabilisation and
Destabilisation. Workshop
on Stochastic Differential Equations and their Applications, 18 May 2007, Nonlinearity
and Random Dynamics. UWI
Mathematics Seminar, 22 September 2006, University of
the West Indies, Complementary
Theoretical and Numerical Analysis of a Perturbed Geometric Brownian Motion. Conference
on Differential and Difference Equations and Applications, 27 June 2006, Rajecké Teplice, Stochastic Delay Differential Equations with Highly Nonlinear
Coefficients: Oscillation. Optimal Stopping with Delayed Information. Probability
Group Reading Seminar, 13 March 2006, Return
to Academic Staff webpage. |
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