Research
Preprints
Time-changed reflected diffusions: subdiffusion, superdiffusion and explosion
Hypocoercivity of Tempered Bouncy Particle Samplers for heavy-tailed targets
· arXiv:2608.29657 · YouTube: Results · YouTube: Ideas & proofs
Monte Carlo Approximations of Time-Nonlocal Diffusions in Bounded Domains
Diffeomorphic Markov chain Monte Carlo: fast mixing for heavy-tailed distributions
Functional central limit theorem for superdiffusive SDEs with stable noise
Limit theorems & random walks Diffusions & SDEs Lévy processes
Central Limit Theorem for ergodic averages of Markov chains & the comparison of sampling algorithms for heavy-tailed distributions
· arXiv:2512.18255 · YouTube: Theory & ULA · YouTube: MCMC applications
Stability of storage processes with general release rates
Critical branching processes with immigration: scaling limits of local extinction sets
Superdiffusive limits for stochastic kinetics driven by self-similar drifts
Published & accepted papers
Multivariate CLT for Lévy processes: convergence rates without moment assumptions
· arXiv:2510.06891 · to appear in Bernoulli (2026) · YouTube: Convergence rates
Limit Theorems for Stochastic Gradient Descent with Infinite Variance
· arXiv:2410.16340 · to appear in Annals of Applied Probability (2026) · YouTube: SGD limit theorems
Subexponential lower bounds for f-ergodic Markov processes
· arXiv:2403.14826 · Probability Theory and Related Fields 194(1): 997-1054 (2026) · YouTube: Results · YouTube: Proofs
Central limit theorem for superdiffusive reflected Brownian motion
· arXiv:2412.14267 · Annals of Applied Probability Vol. 36, No. 2, 1840-1892 (2026) · YouTube: Gaussian fluctuations · PDF
Modeling of Measurement Error in Financial Returns Data
· arXiv:2408.07405 · Stochastic Analysis and Applications 43(6), 716-733 (2025)
Non-asymptotic bounds for forward processes in denoising diffusions: Ornstein-Uhlenbeck is hard to beat
· arXiv:2408.13799 · Annals of Applied Probability Vol. 35, No. 6, 4439-4463 (2025) · YouTube: Setting & results · YouTube: General results & proofs · PDF
Asymptotically optimal Wasserstein couplings for the small-time stable domain of attraction
· arXiv:2411.03609 · to appear in Annales de l’Institut Henri Poincaré - Probabilités et Statistiques (2025), 39 pp · YouTube: Couplings & rates
Lévy processes Stochastic control & coupling Limit theorems & random walks
Stationary entrance chains and applications to random walks
· arXiv:2403.00619 · to appear in Stochastic Processes and their Applications (2025), 36 pp
Fast exact simulation of the first-passage event of a subordinator
· arXiv:2306.06927 · to appear in Stochastic Processes and their Applications (2025), 25 pp · YouTube: Algorithm & complexity · YouTube: Proofs & numerics · Python code · Julia code
Brownian motion with asymptotically normal reflection in unbounded domains: from transience to stability
· arXiv:2303.06916 · Annals of Probability 53(1): 175-222 (2025) · YouTube: Stability & rates · YouTube: Proof ideas
Fast exact simulation of the first passage of a tempered stable subordinator across a non-increasing function
· arXiv:2303.11964 · Stochastic Systems 15(1): 50-87 (2024) · YouTube: Exact simulation · YouTube: Monte Carlo applications · Python code · Julia code
A weak MLMC scheme for Lévy-copula-driven SDEs with applications to the pricing of credit, equity and interest rate derivatives
· arXiv:2211.02528 · Applied Mathematical Finance Vol. 31, No. 2, 57–107 (2024)
Simulation & numerical methods Lévy processes Mathematical finance
When is the convex hull of a Lévy path smooth?
· arXiv:2205.14416 · Annales de l’Institut Henri Poincaré - Probabilités et Statistiques Vol. 60, No 4, 2352–2381 (2024) · YouTube: Smoothness criteria · YouTube: Further results
Optimal Markovian coupling for finite activity Lévy processes
How smooth can the convex hull of a Lévy path be?
· arXiv:2206.09928 · Electronic Journal of Probability, 29: 1-36 (2024) · YouTube: Boundary growth rates
Hölder continuity of the convex minorant of a Lévy process
· arXiv:2207.12433 · Electronic Communications in Probability, 28: 1-12 (2023) · YouTube: Hölder regularity
Reflecting Brownian motion in generalized parabolic domains: explosion and superdiffusivity
· arXiv:2203.00966 · Annales de l’Institut Henri Poincaré - Probabilités et Statistiques Vol. 59, No. 4 (2023) 1813–1843 · YouTube: Results · YouTube: Proofs
Joint density of a stable process and its supremum: regularity and upper bounds
· arXiv:2008.01894 · Bernoulli 29(4), 3443-3469 (2023) · YouTube
Monte Carlo algorithm for the extrema of tempered stable processes
· arXiv:2103.15310 · Advances in Applied Probability 55 (4) , 1362-1389 (2023) · YouTube: Tempered stick-breaking
Simulation of the drawdown and its duration in Lévy models via stick-breaking Gaussian approximation
· arXiv:2011.06618 · Finance & Stochastics, Vol. 26 (2022), 671–732 · YouTube: Gaussian approximation
Simulation & numerical methods Lévy processes Mathematical finance
Asymptotic shape of the concave majorant of a Lévy process
· arXiv:2106.09066 · Annales Henri Lebesgue, Vol. 5 (2022), 779-811 · YouTube: Results
Limit theorems for local times and applications to SDEs with jumps
· arXiv:1910.09501 · Stochastic Processes and their Applications, Vol. 153, 39-55 (2022) · ResearchGate
Convex minorants and the fluctuation theory of Lévy processes
· arXiv:2105.15060 · ALEA, Lat. Am. J. Probab. Math. Stat., 19, 983–999 (2022) · YouTube: Fluctuation theory & SBRT
Geometrically Convergent Simulation of the Extrema of Lévy Processes
· arXiv:1810.11039 · Mathematics of Operations Research 47(2):1141-1168, (2021) · YouTube: Stick-breaking algorithm
A Gaussian approximation theorem for Lévy processes
· arXiv:2104.13855 · Statistics & Probability Letters, Vol. 178 (Nov 2021)
Monte Carlo estimation of the solution of fractional partial differential equations
· arXiv:2012.13904 · Fractional Calculus and Applied Analysis, Vol. 24, no. 1, 278-306 (2021)
Lévy processes on smooth manifolds with a connection
· arXiv:2012.11633 · Electronic Journal of Probability, 26: 1-39 (2021) · YouTube
An algorithm for simulating Brownian increments on a sphere
· arXiv:2012.12018 · Journal of Physics A: Mathematical and Theoretical Vol. 54, no. 11 (2021)
Simulation & numerical methods Diffusions & SDEs Geometry & topology
Stability of overshoots of zero mean random walks
· arXiv:1812.05909 · Electronic Journal of Probability, 25: 1-22 (2020) · Journal
ε -strong simulation of the convex minorants of stable processes and meanders
· arXiv:1910.13273 · Electronic Journal of Probability, 25: 1-33 (2020) · Journal
A note on the exact simulation of spherical Brownian motion
· arXiv:1811.12107 · Statistics & Probability Letters, Vol 165, (October 2020)
Simulation & numerical methods Diffusions & SDEs Geometry & topology
Non-asymptotic bounds for sampling algorithms without log-concavity
· arXiv:1808.07105 · Annals of Applied Probability, Vol. 30, no. 4, pp. 1534-1581 (2020)
Exact Simulation of the Extrema of Stable Processes
· arXiv:1806.01870 · Advances in Applied Probability, 51(4), 967-993 (2019) · Python code · Julia code
Asymptotic variance for random walk Metropolis chains in high dimensions: logarithmic growth via the Poisson equation
· arXiv:1707.08510 · Advances in Applied Probability, 51(4), 994-1026 (2019)
Invariance principle for non-homogeneous random walks
· arXiv:1801.07882 · Electronic Journal of Probability, 24:1-38 (2019)
Projections of spherical Brownian motion
· arXiv:1806.00266 · Electronic Communications in Probability Vol. 23 (2018), 12 pp
On the Poisson equation for Metropolis-Hastings chains
· Bernoulli Vol. 24, no. 3 (2018), 2401–2428
A radial invariance principle for non-homogeneous random walks
· Electronic Communications in Probability Vol. 23 (2018), 11 pp
On the policy improvement algorithm in continuous time
Procuring load curtailment from local customers under uncertainty
· Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences (August 2017), doi: 10.1098/rsta.2016.0311
Anomalous recurrence properties of many-dimensional zero-drift random walks
· Advances in Applied Probability Vol. 48, no. A (2016), 99--118
Joint asymptotic distribution of certain path functionals of the reflected process
· Electronic Communications in Probability Vol. 21 (2016), 1–18
Brownian manifolds, negative type and geo-temporal covariances
· Communications on Stochastic Analysis Vol. 10, no. 4 (2016)
A new look at short-term implied volatility in asset price models with jumps
· Mathematical Finance Vol. 26, Issue 1 (January 2016), 149–183
An integral equation for Root’s barrier and the generation of Brownian increments
· Annals of Applied Probability Vol. 25, no. 4 (2015), 2039–2065
Coupling and tracking of regime-switching martingales
· Electronic Journal of Probability Vol. 20 (2015), 39pp
Randomisation and recursion methods for mixed-exponential Lévy models, with financial applications
· Journal of Applied Probability Vol. 52, Issue 4 (December 2015), 1076–1096
Mathematical finance Lévy processes Simulation & numerical methods
Markov chain approximations to scale functions of Lévy processes
· Stochastic Processes and their Applications Vol. 125, Issue 10 (October 2015), 3932– 3957
On the loss of the semimartingale property at the hitting time of a level
· Journal of Theoretical Probability Vol. 28, Issue 3 (September 2015), 892–922
Buffer-overflows: joint limit laws of undershoots and overshoots of reflected processes
· Stochastic Processes and their Applications Vol. 125, Issue 8 (August 2015), 2937– 2954
Asymptotic independence of three statistics of maximal segmental scores
· Statistics & Probability Letters Vol. 99 (April 2015), 185–191
Arbitrage-free prediction of the implied volatility smile
· Risk Magazine, Technical Paper section, 30 April (2014)
Markov Chain approximations for transition densities of Lévy processes
· Electronic Journal of Probability Vol. 19 (2014), 1–37
Mirror and synchronous couplings of geometric Brownian motions
· Stochastic Processes and their Applications Vol. 124, no. 2 (2014), 1055–1069
Large deviations for the extended Heston model: the large-time case
· Asia-Pacific Financial Markets Vol. 21 (2014), 263–280
Empirical asset pricing with non-linear risk premia
· Journal of Financial Econometrics Vol. 12, no. 3 (2014), 479–506
A note on delta hedging in markets with jumps
· IMA Journal of Applied Mathematics Vol. 79, no. 2 (2014), 300–312
Continuously monitored barrier options under Markov processes
· Mathematical Finance Vol. 23, no. 1 (2013), 1–38
Large deviations and stochastic volatility with jumps: asymptotic implied volatility for affine models
· Stochastics Vol. 85, no. 2 (2013), 321–345
Convergence of integral functionals of one-dimensional diffusions
· Electronic Communications in Probability Vol. 17 (2012), 1–13
On the limit distributions of continuous-state branching processes with immigration
· Stochastic Processes and their Applications Vol. 122, no. 6 (2012), 2329–2345
On the drawdown of completely asymmetric Lévy processes
· Stochastic Processes and their Applications Vol. 122, no. 11 (2012), 3812–3836
Martingale property of generalized stochastic exponentials
· Séminaire de Probabilités, XLIV, Lecture Notes in Mathematics Vol. 2046 (2012), 41–59
Deterministic criteria for the absence of arbitrage in one-dimensional diffusion models
· Finance & Stochastics Vol. 16, no. 2 (2012), 225–247
On the martingale property of certain local martingales
· Probability Theory and Related Fields Vol. 152, no. 1 (2012), 1–30
A note on essential smoothness in the Heston model
· Finance & Stochastics Vol. 15 (2011), 781–784
A note on a paper by Wong and Heyde
· Journal of Applied Probability Vol. 48, no. 3 (2011), 811–819
Volatility derivatives in market models with jumps
· International Journal of Theoretical and Applied Finance Vol. 14, no. 07 (2011), 1159–1193
Asymptotic formulae for implied volatility in the Heston model
· Proceedings of the Royal Society A Vol. 466, no. 2124 (2010), 3593–3620
Approximating Lévy processes with a view to option pricing
· International Journal of Theoretical and Applied Finance Vol. 13, Issue 1 (2010), 63–91
Lévy processes Simulation & numerical methods Mathematical finance
Globally optimal parameter estimates for non-linear diffusions
Local time and the pricing of time-dependent barrier options
Spectral methods for volatility derivatives
· arXiv:0905.2091 · Quantitative Finance Vol. 9, Issue 6 (2009), 663–692
A stochastic volatility model for risk-reversals in foreign exchange
· International Journal of Theoretical and Applied Finance Vol. 12, Issue 6 (2009), 877–899
Spectral properties of trinomial trees
· Proceedings of the Royal Society A Vol. 463, no. 2083 (2007), 1681–1696
Simplicial structures of knot-complements
· Mathematical Research Letters Vol. 12, no. 5-6 (2005), 843–856
Triangulations of fibre-free Haken 3-manifolds
· Pacific Journal of Mathematics Vol. 219, no. 1 (2005), 139–186
Triangulations of Seifert fibred manifolds
· Mathematische Annalen Vol. 330, no. 2 (2004), 235–273
Simplifying triangulations of the 3-sphere
· Pacific Journal of Mathematics Vol. 208, no. 2 (2003), 291–324
Edited volumes
Probability, Analysis and Number Theory: Papers in Honour of N. H. Bingham
· Advances in Applied Probability Special Volume 48A, 2016 · Journal
Spectral and Cubature Methods in Finance and Econometrics
· special issue of International Journal of Theoretical and Applied Finance, 2011
Book chapters
Reflecting random walks in curvilinear wedges
· arXiv:2001.06685 · In and Out of Equilibrium 3: Celebrating Vladas Sidoravicius, in Series Progress in Probability, Springer International Publishing (2021), Editors Maria Eulália Vares, Roberto Fernández, Luiz Renato Fontes, Charles M. Newman, 637-675
Exotic derivatives in stochastic volatility models with jumps
· arXiv:0912.2595 · Advanced Mathematical Methods for Finance, Springer, 2011, Editors G. Di Nunno, B. Oksendal, 455–508
Conference proceedings
On additive time-changes of Feller processes
· arXiv:0909.4881 · Progress in Analysis and its Applications, Proceedings of the 7th International Isaac Congress, Imperial College London UK, 13 - 18 July 2009, 431–437
Unpublished manuscripts
Martingale approach to control for general jump processes
Invariance principles for local times in regenerative settings
Coupling and a generalised Policy Iteration Algorithm in continuous time
Stationarity of entrance Markov chains and level-crossings of random walks
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