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Personal profile

Research interests

I have several main themes of research. I am generally interested in the theory of Lévy processes and their insertion into a wide variety of (applied) probability models arising in: optimal stopping and stochastic control problems, queuing theory, (numerical) stochastic differential equations and financial and actuarial mathematics. More recently I have been interested in questions pertaining to the (potential) analysis of self-similar Markov processes. I also have broad and active interests in the theory of branching and coalescing structures. These include (spatial) growth properties of branching random walks, branching particle diffusions, superprocesses and continuous-state branching processes, fragmentation processes and stochastic coalescent models.

My interest in these all of these subfields of probability is largely, but not exclusively, motivated by elegant path decompositions. I am also drawn to anything that can be proved in a beautiful way using a martingale.

Educated at the Universities of Oxford and Sheffield, and having held previous academic positions at the London School of Economics, Edinburgh University, Utrecht University and at Heriot Watt University, I came to Bath in 2006. I am the co-founder and current director of of Prob-L@B: the Probability Laboratory at Bath.

Fingerprint Fingerprint is based on mining the text of the person's scientific documents to create an index of weighted terms, which defines the key subjects of each individual researcher.

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Lévy Process Mathematics
Scale Function Mathematics
Martingale Mathematics
Self-similar Processes Mathematics
Stable Process Mathematics
Markov Process Mathematics
Branching Mathematics
Continuous-state Branching Process Mathematics

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Projects 2007 2023

Rutherford Fund Strategic Partner Grant

Kyprianou, A. & Milewski, P.

31/03/1830/03/19

Project: Central government, health and local authorities

Wolfson Merit Award

Kyprianou, A.

1/02/1831/01/23

Project: Research council

safety
neutrons
nuclear fission
reactor cores
industries

EPSRC Centre for Doctoral Training in Statistical Applied Mathematics at Bath (SAMBa)

Kyprianou, A., Milewski, P. & Wood, S.

1/05/1431/10/22

Project: Research-related fundingPGR Training Grant

Research Output 1996 2018

Conditioned real self-similar Markov processes

Kyprianou, A., Rivero Mercado, V. & Satitkanitkul, W., 18 Apr 2018, In : Stochastic Processes and their Applications.

Research output: Contribution to journalArticle

Self-similar Processes
Stable Process
Markov Process
Markov processes
Conditioning
1 Citations

Deep factorisation of the stable process II: potentials and applications

Kyprianou, A., Rivero Mercado, V. & Sengul, B., 1 Feb 2018, In : Annales de l'Institut Henri Poincaré: Probabilités et Statistiques. 54, 1, p. 343-362

Research output: Contribution to journalArticle

Stable Lévy processes, self-similarity and the unit ball

Kyprianou, A. E., 2018, In : Alea. 15, 1, p. 617-690 74 p.

Research output: Contribution to journalArticle

Unbiased `walk-on-spheres' Monte Carlo methods for the fractional Laplacian

Kyprianou, A., Osojnik, A. & Shardlow, T., 1 Jul 2018, In : IMA Journal of Numerical Analysis. 38, 3, p. 1550-1578

Research output: Contribution to journalArticle

Open Access
Fractional Laplacian
Walk
Monte Carlo method
Stable Process
Monte Carlo methods

Universality in a class of fragmentation-coalescence processes

Kyprianou, A. E., Pagett, S. W. & Rogers, T., 1 May 2018, In : Annales de l'Institut Henri Poincaré: Probabilités et Statistiques. 54, 2, p. 1134-1151

Research output: Contribution to journalArticle

Open Access
File
Coalescence
Fragmentation
Universality
Breakup
Thermodynamic Limit

Thesis

Asymptotic properties of fragmentation processes

Author: Knobloch, R., 1 Jan 2011

Supervisor: Kyprianou, A. (Supervisor) & Harris, S. (Supervisor)

Student thesis: Doctoral ThesisPhD

File

Branching Diffusions on the Boundary and the Interior of Balls

Author: Hesse, M., 17 Dec 2013

Supervisor: Kyprianou, A. (Supervisor) & Harris, S. (Supervisor)

Student thesis: Doctoral ThesisPhD

File

Fragmentation-Coalescence Processes: Theory and Applications

Author: Pagett, S., 26 Apr 2017

Supervisor: Rogers, T. (Supervisor) & Kyprianou, A. (Supervisor)

Student thesis: Doctoral ThesisPhD

File

Optimal Stopping Problems for the Maximum Process

Author: Ott, C., 31 Dec 2013

Supervisor: Kyprianou, A. (Supervisor)

Student thesis: Doctoral ThesisPhD

File

Superprocesses and Large-Scale Networks

Author: Eckhoff, M., 26 Nov 2014

Supervisor: Kyprianou, A. (Supervisor) & Morters, P. (Supervisor)

Student thesis: Doctoral ThesisPhD

File