Branching Random Walk: Seneta-Heyde norming. (with
J.D. Biggins)
In
Trees
(B.Chauvin, S. Cohen, and A. Rouault, eds) Birkhaser, Basel, 1995.
Seneta-Heyde norming in the branching random walk.
(with J.D. Biggins).
Annals of Probabability (1997), 25, 337-360.
Slow variation and uniqueness of solutions to the functional equation
in the branching random walk.
Journal of Applied Probability (1998), 35, 795-802.
A note on branching Lévy processes.
Stochastic Processes and their Applications (1999), 82, 1-14.
Martingale Convergence and the Stopped Branching Random Walk.
Probability Theory and Related Fields (2000), 116, 405--419.
Martingale convergence and the functional equation in the multi-type branching random walk.
(with
A. Rahimzadeh Sani).
Bernoulli. (2001), 7(4), 593--604.
A note on the alpha-quantile option.
(with
Laura Ballotta).
Applied Mathematical Finance (2001), 8, 137--144.
Perpetual options and Canadization through fluctuation theory. (with Martijn Pistorius).
Annals of Applied Probability (2003), 13(3), 1077-1098.
Law of the iterated logarithm for oscillating random walks conditioned to stay
non-negative. (with B. Hambly and G.Kersting)
Stochastic Processes and their Applications (2003), Vol 108/2 pp 327-343.
Some calculations for Israeli options.
Finance and Stochastics. (2004), 8, 73 - 86.
Local extinction versus local exponential growth for
spatial branching processes. (with Janos Englander)
Annals of Probability (2004), 32, 78-99.
Exit problems for spectrally negative Lévy processes adn applications to (Canadized) Russian options. (with F.Avram and Martijn Pistorius).
Annals of Applied Probability (2004), 14(1), 215-238.
Travelling wave solutions to the K-P-P equation: alternitives
to Simon Harris' probabilistic analysis.
Annales de l'Instut Henri Poincaré. (2004), 40(1), 53-72.
Ruin probabilties and overshoots for general Lévy insurance risk process.
(with C. Kluppelberg
and Ross Maller).
Annals of Applied Probability. (2004), 14(4),
1766-1801.
Measure change in multitype branching.
(with J.D. Biggins).
Advances in Applied Probability (2004), 36(2) 544-581.
A martingale review of some fluctuation theory for spectrally negative Lévy processes. (with
Z. Palmowski).
Séminaire de Probabilité XXXVIII, 16-29.
Further calculations for Israeli options. (with Erik Baurdoux).
Stochastics. (2004), 76, 549-569.
Asymptotic radial speed of the support of supercritical
branching Brownian motion and super-Brownian motion in R^d.
Markov Processes and Related Fields. (2005), 11, 145-156.
Finite expiry Russian options.
(with Kees van Schaik and
Hans Duistermaat).
Stochastic Processes and their Applications. (2005), Vol 115/4, 609-638..
Lévy processes in finance distinguished by their coarse and fine path properties. (with Ronnie Loeffen).
In Exotic option pricing and advanced Lévy models. Eds. A. Kyprianou, W. Schoutens and P. Wilmott. Wiley, 2005.
The smoothing transform:
the boundary case. (with J.D. Biggins).
Electronic Journal of Probability (2005), 10,
609-631.
Some remarks on first passage of Lévy process, the American put and pasting principles.
(with Larbi Alili).
Annals of Applied Probability (2005), 15, 2062--2080.
On the Novikov-Shiryaev optimal stopping problem in continuous time. (with B. Surya).
Electronic Communications in Probability (2005), 10,
146-154.
Further probabilistic analysis of the Fisher-Kolmogorov-Petrovskii-Piscounov equation: one sided travelling waves.
(with John Harris and S. C. Harris).
Annales de l'Instut Henri Poincaré (2006), 42, 125-145.
Overshoots and Undershoots of Lévy process
(with Ron Doney).
Annals of Applied Probability (2006), 16, 91-106.
First passage of reflected strictly stable processes.
ALEA (2006), 2, 119-123.
On extreme ruinous behaviour of Lévy insurance risk processes. (with C. Kluppelberg).
Journal of Applied Probability (2006), 43, 594-598.
Quasi-stationary distributions for Lévy process. (with Z. Palmowski).
Bernoulli (2006), 12, 571-581.
Principles of smooth and continuous fit in the determination of endogenous bankruptcy levels. (with B. Surya).
Finance and Stochastics (2007), 11, 131-152.
Pricing Isreali options: a pathwise approach.
(with C. Kuhn and K. van Schaik).
Stochastics (2007), 79, 117-137.
Distributional study of De Finetti's
dividend problem for a general
Lévy insurance risk process. (with Z. Palmowski)
Journal of Applied Probability. (2007), 44, 428-443.
A note on the change of variable formula with local time-space for bounded variation Lévy processes. (With B. Surya).
Séminaire de Probabilité
XL. 97-105.
Callable puts as composite exotic options.
(with C. Kuhn).
Mathematical Finance (2007), 17, 487-502.
The McKean stochastic game driven by a spectrally
negative Lévy process. (with Erik Baurdoux).
Electronic Journal of Probability. (2008), Paper no. 8, 173-197.
Fluctuations of spectrally negative Markov Additive Processes.
(with Z. Palmowski).
Séminaire de Probabilité XLI. 121-135.
On the parabolic generator of a general one-dimensional Lévy process. (with Nathalie Eisenbaum).
Electronic Communications in Probability (2008), Paper no. 20, 198-209.
Special, conjugate and complete scale
functions for spectrally negative Lévy processes. (with V. Rivero).
Electronic Journal of Probability (2008), Paper no 57, 1672-1701.
Continuous state branching processes and self-similarity. (with Juan Carlos Pardo).
Journal of Applied Probability (2008), 45 (4), 1140-1160.
Analysis of stochastic
fluid queues driven by local
time processes. (with Takis Konstantopoulos, Paavo Salminen and Marina Sirvio (née Kozlova)).
Advances of Applied Probability (2008), vol. 40 (4), 1072-1103.
Branching processes in random environment die slowly. (with V.Vatutin).
Discrete Mathematics & Theoretical Computer Science Proceedings Fifth Colloquium on Mathematics and Computer Science (2008), 375-396.
Some explicit identities associated with positive
self-similar Markov processes. (with Loic Chaumont and Juan Carlos Pardo).
Stochastic Processes and Their Applications (2009), 119/3, 980-1000.
The Shepp-Shiryaev stochastic game driven by a spectrally negative Lévy process. (with Erik Baurdoux).
Theory of Probability and Its Applications (Teoriya Veroyatnostei i ee Primeneniya) (2009), 53, 481-499..
General tax structures and the Lévy insurance risk model. (with Xiaowen Zhou).
Journal of Applied Probability (2009), 46, 1146-1156.
A note on scale functions and the time value of ruin for Lévy insurance risk processes. (with Enrico Biffis).
Insurance Mathematics and Economics (2010), 46, 85-91.
Refracted Lévy processes. (with R. Loeffen).
Annales de l'Instut Henri Poincaré (2010), 46, 24-44.
Strong law of large numbers for fragmentation processes.
(with S.C. Harris and R.Knobloch).
Annales de l'Instut Henri Poincaré (2010), 46, 119-134..
Strong law of large numbers for branching diffusions. (with Janos Englander and Simon Harris).
Annales de l'Instut Henri Poincaré (2010), 46, 279-298.
The Wiener-Hopf decomposition.
Encyclopedia of Quantitative Finance, published by Wiley.
Lévy processes.
Encyclopedia of Quantitative Finance, published by Wiley.
Exact and asymptotic n-tuple laws at first and last passage. (with V. Rivero and Juan Carlos Pardo).
Annals of Applied Probability (2010), Vol. 20, No. 2, 522-564.
Convexity and smoothness of scale functions
and de Finetti's control problem. (with V. Rivero and Renming Song).
Journal of Theoretical Probability (2010), 23, 547-564.
Old and new examples of scale functions for spectrally negative Lévy processes. (with F. Hubalek).
Sixth Seminar on Stochastic Analysis, Random Fields and Applications, eds R. Dalang, M. Dozzi, F. Russo. Progress in Probability, Birkhäuser (2010), 119-146.
The Gapeev--Kühn stochastic game driven by a spectrally positive
Lévy process. (with Erik Baurdoux and Juan Carlos Pardo).
Stochastic Processes and their Applications (2011), 121/6, 1266-1289.
The prolific backbone for supercritical superdiffusions. (with Julien Berestycki and Antonio Murillo).
Stochastic Processes and their Applications (2011), 121/6, 1315-1331.
A Ciesielski-Taylor type identity for positive self-similar Markov processes (with Pierre Patie).
Annales de l'Instut Henri Poincaré (2011), 47/3, 917-928.
Smoothness of scale functions for spectrally negative Lévy processes (with Terence Chan and Mladen Savov).
Probability Theory and Related Fields (2011), 150, 691-708.
On the excursions of reflected local time processes and stochastic fluid queues. (with Takis Konstantopoulos and Paavo Salminen).
Journal of Applied Probability (2011), 48A, 79-98.
Travelling waves and homogeneous fragmentation (with Julien Berestycki and Simon Harris).
Annals of Applied Probability. (2011), 21, 1749-1794.
A Wiener-Hopf Monte Carlo simulation technique for Lévy process (with Alexey Kuznetsov, Juan Carlos Pardo and Kees van Schaik).
Annals of Applied Probability. (2011), 21, 2171-2190.
Backbone decomposition for continuous-state branching processes with immigration. (with Yanxia Ren).
Statistics and Probability Letters. (2012), 82, 139-144.
Fluctuation theory and exit systems for positive self-similar Markov processes (with Loic Chaumont, V. Rivero and Juan Carlos Pardo).
Annals of Probability (2012), 40, 245-279.
Optimal control with absolutely continuous strategies
for spectrally negative Lévy processes. (with Ronnie Loeffen and Jose-Luis Pérez).
Journal of Applied Probability (2012), 49, 150-166.
An optimal stopping problem for fragmentation processes. (with Juan Carlos Pardo).
Stochastic Processes and their Applications. (2012), 122, 1210-1225.
Meromorphic Lévy processes and their fluctuation identities (with Alexey Kuznetsov, Juan Carlos Pardo).
Annals of Applied Probability. (2012), 22, 1101-1135.
Supercritical super-Brownian
motion with a general branching mechanism and travelling waves (with Antonio Murillo-Salas, Rongli Liu and Yanxia Ren).
Annales de l'Instut Henri Poincaré. (2012), 48, 661-687.
Super-Brownian motion: Lp-convergence of martingales
through the pathwise spine decomposition. (with Antonio Murillo-Salas).
In Advances in Superprocesses and Nonlinear PDEs
Series: Springer Proceedings in Mathematics & Statistics, Vol. 38
Englander, Janos; Rider, Brian C. (Eds.), 2013.
An application of the backbone decomposition to supercritical super-Brownian motion with a barrier. (with Antonio Murillo-Salas and Jose-Luis Pérez).
Journal of Applied Probability. (2012), 49, 671-684.
Spectrally negative Lévy processes perturbed
by functionals of their running supremum (with Curdin Ott).
Journal of Applied Probability (2012), 49, 1005-1014.
On optimal dividends in the dual model
(with Erhan Bayraktar and Kazutoshi Yamazaki).
ASTIN Bulletin (2013), 43, 359-372.
Pricing of Contingent
Convertibles under Smile Conform
Models. (with José Manuel Corcuera, Jan de Spiegeleer, Albert Ferreiro-Castilla, Dillip Madan and Wim Schoutens).
Journal of Credit Risk (2013), 9(3), 121-140.
Multilevel Monte Carlo simulation for Lévy processes based on the Wiener-Hopf factorisation (with Albert Ferreiro-Castilla, Rob Scheichl and Gowri Suryanarayana).
Stochastic Processes and its Applications (2014), 124, 985-1010.
Optimal dividends in the dual model under transaction costs (with Erhan Bayraktar and Kazutoshi Yamazaki).
Insurance: Mathematics and Economics (2014), 54, 133-143.
Hitting distributions of alpha-stable processes via path censoring and self-similarity (with Juan Carlos Pardo and Alex Watson).
Annals of Probability. (2014), 42, 398-430.
A capped optimal stopping problem for the maximum process (with Curdin Ott).
Acta Applicandae Mathematicae. (2014), 129, 147-174.
The total mass of super-Brownian motion upon exiting balls and Sheu's compact support condition.
(with Marion Hesse).
Stochastic Processes and its Applications (2014), 124, 2003-2022.
The hitting time of zero for a stable process (with Alexey Kuznetsov, Juan Carlos Pardo and Alex Watson).
Electronic Journal of Probability (2014), 19, 1-26.
Survival of homogenous fragmentation processes with killing. (with Robert Knobloch).
Annales de l'Instut Henri Poincaré(2014), 50, 476-491.
New families of subordinators with explicit transition probability semigroup. (with James Burridge, Mateusz Kwasnicki, Alexey Kuznetsov.).
Stochastic Processes and their Applications (2014), 124, 3480-3495.
Occupation times of refracted Lévy processes (with Juan Carlos Pardo and Jose-Luis Pérez).
Journal of Theoretical Probability. (2014), 27, 1292-1315.
The extended hypergeometric class of Lévy processes (with Juan Carlos Pardo and Alex Watson).
Journal of Applied Probability. (2014), 51A, 391-408.
The backbone decomposition for spatially dependent supercritical superprocesses (with Jose-Luis Pérez and Yanxia Ren).
Séminaire de Probabilité XLVI. (2015), 33-60.
Potentials of stable processes (with Alex Watson).
Séminaire de Probabilité XLVI. (2015), 333-344.
Spines, skeletons and the Strong Law of Large Numbers for superdiffusions (with Maren Eckhoff and Matthias Winkel).
Annals of Probability.
(2015), Vol. 43, No. 5, 2594-2659.
Branching Brownian motion in a strip: survival near criticality.
(with Simon Harris and Marion Hesse).
Annals of Probability. (2016), Vol. 44, No. 1, 235-275.
An Euler-Poisson Scheme for Lévy driven SDEs (with Albert Ferreiro-Castilla and Rob Scheichl).
Journal of Applied Probability. (2016), 53, 262-278.
UK universities find a cash cow in the financial fall-out
The Conversation. (See also the longer version: The UK financial mathematics M.Sc.)
Deep factorisation of the stable process.
Electronic Journal of Probability. (2016), Volume 21 paper no. 23, 1-28..
More on hypergeometric Lévy processes
(with Emma Horton).
Advances in Applied Probability (2016), 48A, 153 - 158.
Optimal prediction for positive self-similar Markov processes (With Erik Baurdoux and Curdin Ott).
Electronic Journal of Probability. (2016), Volume 21 paper no. 48, 1-24.
Perpetual integrals for Lévy processes (with Leif Döring).
Journal of Theoretical Probability
(2016), Volume 29, Issue 3, pp 1192-1198.
The largest fragment of a homogeneous fragmentation process
(With Peter Mörters and Francis Lane).
Journal of Statistical Physics. (2017), 166, 1226-1246.
Real self-similar processes started from the origin (with Steffen Deriech and Leif Döring).
Annals of Probability. (2017), Volume 45, No. 3, 1952-2003.
Conditioning subordinators embedded in
Markov processes. (with Victor Rivero,
and Bati Sengul
).
Stochastic Processes and their Applications. (2017), 127, 1234-1254.
A phase transition in excursions from infinity of the "fast" fragmentation-coalescence process.
(with Steven Pagett, Tim Rogers and Jason Schweinsberg).
Annals of Probability. (2017),
Volume 45, No. 6A, 3829-3849.
Deep factorisation of the stable process II: potentials and applications. (with Victor M. Rivero and Bati Sengul).
Annales de l'Instut Henri Poincaré. (2018), Vol. 54, No. 1, 343-362.
Universality in a class of fragmentation-coalescence processes. (with Steven Pagett and Tim Rogers).
Annales de l'Instut Henri Poincaré. (2018), Vol. 54, No. 2, 1134-1151.
Almost sure growth of supercritical multi-type continuous state branching process (With Sandra Palau and Yanxia Ren).
ALEA, Lat. Am. J. Probab. Math. Stat. (2018),
15, 409-428
Stable processes, self-similarity and the unit ball
ALEA, Lat. Am. J. Probab. Math. Stat. (2018),
15, 617-690.
Unbiased "walk-on-spheres" Monte Carlo methods for the fractional Laplacian
(With Ana Osojnik and Tony Shardlow).
IMA J. Numer. Anal. (2018), 38 no. 3, 1550-1578.
Stable windings at the origin.
(With Stavros Vakeroudis).
Stochastic Processes and their Applications (2018), 128, 4309-4325.
Extinction properties of multi-type continuous-state branching processes
(With Sandra Palau).
Stochastic Processes and their Applications (2018), 128 3466–3489.
Conditioned real self-similar Markov processes. (with Victor M. Rivero and Weerapat Satitkanitkul).
Stochastic Processes and their Applications (2019), 129, 954-977.
Multi-species neutron transport equation.
(with Alex M.G. Cox, Simon C. Harris and Emma Horton).
Journal of Statistical Physics (2019), 176(2), 425-455.
Skeletal stochastic differential equations for continuous-state branching process
(With Dorottya Fekete and Joaquin Fontbona).
Journal of Applied Probability (2019), 56, 1122-1150.
Entrance and exit at infinity for stable jump diffusions (with Leif Döring).
Annals of Probability
(2020), Vol. 48, No. 3, 1220-1265
Entrance laws at the origin of self-similar Markov processes in high dimensions. (with Victor M. Rivero, Bati Sengul and Ting Yang ) .
Transactions of the American Mathematical Society (2020) Vol. 373 (9), 6227-6299
Stable processes conditioned to avoid an interval (with Leif Döring and Philip Weissmann).
Stochastic Processes and their Applications (2020), Vol 130 no. 2, 471–487.
Deep factorisation of the stable process III: radial excursion theory and the point of closest reach.
(with Victor M. Rivero and Weerapat Satitkanitkul).
To appear in Potential Analysis
Stochastic Methods for the Neutron Transport Equation I: Linear Semigroup asymptotics. (with Emma Horton and Denis Villemonais) .
To appear in Annals of Applied Probability.
Stochastic Methods for the Neutron Transport Equation II: Almost sure growth. (with Emma Horton and Simon Harris) .
To appear in Annals of Applied Probability.
Skeletal stochastic differential equations for superprocesses
(With Dorottya Fekete and Joaquin Fontbona).
To appear in Advances/Journal of Applied Probability.
Double hypergeometric Lévy processes and self-similarity
(With Juan Carlos Pardo and Matija Vidmar).
To appear in Advances/Journal of Applied Probability.
