185 citations · 819 across the 64 of their papers we have counts for
73 papers · 1 filter
Many-to-few for non-local branching Markov process
Simon C. Harris, Emma Horton, Ellen Powell +1
We provide a many-to-few formula in the general setting of non-local branching Markov processes. This formula allows one to compute expectations of k-fold sums over functions of th…
A lifetime of excursions through random walks and Lévy processes
Loïc Chaumont, Andreas Kyprianou
In celebration of Professor Ron Doney's 80th birthday, we provide a summary of his academic career and contributions to probability theory, as one of the UK's leading probabilists…
The Doob-McKean identity for stable Lévy processes
Andreas E. Kyprianou, Neil O'Connell
We re-examine the celebrated Doob--McKean identity that identifies a conditioned one-dimensional Brownian motion as the radial part of a 3-dimensional Brownian motion or, equivalen…
Multitype -coalescents
Samuel G. G. Johnston, Andreas E. Kyprianou, Tim Rogers
Consider a multitype coalescent process in which each block has a colour in . Individual blocks may change colour, and some number of blocks of various colours may…
Yaglom limit for critical neutron transport
Simon C. Harris, Emma Horton, Andreas E. Kyprianou +1
We consider the classical Yaglom limit theorem for a branching Markov process , with non-local branching mechanism in the setting that the mean semigroup is cri…
General path integrals and stable SDEs
Sam Baguley, Leif Doering, Andreas Kyprianou
The theory of one-dimensional stochastic differential equations driven by Brownian motion is classical and has been largely understood for several decades. For stochastic different…
Monte-Carlo Methods for the Neutron Transport Equation
Alexander M. G. Cox, Simon C. Harris, Andreas E. Kyprianou +1
This paper continues our treatment of the Neutron Transport Equation (NTE) building on the work in [arXiv:1809.00827v2], [arXiv:1810.01779v4] and [arXiv:1901.00220v3], which descri…
Oscillatory attraction and repulsion from a subset of the unit sphere or hyperplane for isotropic stable Lévy processes
Mateusz Kwaśniki, Andreas E. Kyprianou, Sandra Palau +1
Suppose that is a closed set of the unit sphere in dimension , which has positive surface measure. We constr…
An optimal stopping problem for spectrally negative Markov additive processes
Mine Caglar, Andreas E. Kyprianou, Ceren Vardar-Acar
Previous authors have considered optimal stopping problems driven by the running maximum of a spectrally negative Lévy process , as well as of a one-dimensional diffusion. Many…
Attraction to and repulsion from a subset of the unit sphere for isotropic stable Lévy processes
Andreas E. Kyprianou, Sandra Palau, Tsogzolmaa Saizmaa
Taking account of recent developments in the representation of -dimensional isotropic stable Lévy processes as self-similar Markov processes, we consider a number of new ways to…
Double hypergeometric Lévy processes and self-similarity
Andreas E. Kyprianou, Juan Carlos Pardo, Matija Vidmar
Motivated by a recent paper of Budd, where a new family of positive self-similar Markov processes associated to stable processes appears, we introduce a new family of Lévy processe…
Skeletal stochastic differential equations for superprocesses
Dorottya Fekete, Joaquin Fontbona, Andreas E. Kyprianou
It is well understood that a supercritical superprocess is equal in law to a discrete Markov branching process whose genealogy is dressed in a Poissonian way with immigration which…
Stochastic Methods for the Neutron Transport Equation II: Almost sure growth
Simon C. Harris, Emma Horton, Andreas E. Kyprianou
The neutron transport equation (NTE) describes the flux of neutrons across a planar cross-section in an inhomogeneous fissile medium when the process of nuclear fission is active.…
Entrance laws at the origin of self-similar Markov processes in high dimensions
Andreas E. Kyprianou, Victor Rivero, Bati Şengül +1
In this paper we consider the problem of finding entrance laws at the origin for self-similar Markov processes in , killed upon hitting the origin. Under mild assumpt…
Stochastic Methods for the Neutron Transport Equation I: Linear Semigroup asymptotics
Emma Horton, Andreas E. Kyprianou, Denis Villemonais
The Neutron Transport Equation (NTE) describes the flux of neutrons through an inhomogeneous fissile medium. In this paper, we reconnect the NTE to the physical model of the spatia…
Multi-species neutron transport equation
Alex M. G. Cox, Simon C. Harris, Emma Horton +1
The Neutron Transport Equation (NTE) describes the flux of neutrons through inhomogeneous fissile medium. Whilst well treated in the nuclear physics literature (cf. [9, 27]), the N…
Stable Lévy processes in a cone
Andreas E. Kyprianou, Victor Rivero, Weerapat Satitkanitkul
Bañuelos and Bogdan (2004) and Bogdan, Palmowski and Wang (2016) analyse the asymptotic tail distribution of the first time a stable (Lévy) process in dimension exists a…
Stable processes conditioned to avoid an interval
Leif Doering, Andreas E Kyprianou, Philip Weissmann
Conditioning Markov processes to avoid a domain is a classical problem that has been studied in many settings. Ingredients for standard arguments involve the leading order tail asy…
Entrance and exit at infinity for stable jump diffusions
Leif Doering, Andreas E. Kyprianou
In his seminal work from the 1950s, William Feller classified all one-dimensional diffusions on in terms of their ability to access the boundary (Felle…
Stable processes, self-similarity and the unit ball
Andreas E. Kyprianou
Around the 1960s a celebrated collection of papers emerged offering a number of explicit identities for the class of isotropic stable processes in one and higher dimensions; these…
Deep factorisation of the stable process III: Radial excursion theory and the point of closest reach
Andreas Kyprianou, Victor Rivero, Weerapat Satitkanitkul
In this paper, we continue our understanding of the stable process from the perspective of the theory of self-similar Markov processes in the spirit of the recent papers of Kyprian…
Skeletal stochastic differential equations for continuous-state branching process
Dorottya Fekete, Joaquin Fontbona, Andreas E. Kyprianou
It is well understood that a supercritical continuous-state branching process (CSBP) is equal in law to a discrete continuous-time Galton Watson process (the skeleton of prolific i…
Stable windings at the origin
A. E. Kyprianou, S. Vakeroudis
In 1996, Bertoin and Werner [5] demonstrated a functional limit theorem, characterising the windings of pla- nar isotropic stable processes around the origin for large times, there…
Extinction properties of multi-type continuous-state branching processes
Andreas Kyprianou, Sandra Palau
Recently in Barczy, Li and Pap (2015), the notion of a multi-type continuous-state branching process (with immigration) having d-types was introduced as a solution to an d-dimensio…