Research outputs


The Lyapunov spectrum for conditioned random dynamical systems

Authors: Matheus M. Castro, Dennis Chemnitz, Hugo Chu, Maximilian Engel, Jeroen S. W. Lamb, Martin Rasmussen

On the quasi-ergodicity of absorbing Markov chains with unbounded transition densities, including random logistic maps with escape

Authors: Matheus M. Castro, Vincent P. H. Goverse, Jeroen S. W. Lamb, Martin Rasmussen

The mean field limit of stochastic differential equation systems modelling grid cells

Authors: José A. Carrillo, Andrea Clini, Susanne Solem

Porous media equations with nonlinear gradient noise and Dirichlet boundary conditions

Authors: Andrea Clini

The free energy principle made simpler but not too simple

Authors: Karl Friston, Lancelot Da Costa, Noor Sajid, Conor Heins, Kai Ueltzhöffer, Grigorios A. Pavliotis, Thomas Parr

Geometric Methods for Sampling, Optimisation, Inference and Adaptive Agents

Authors: Alessandro Barp, Lancelot Da Costa, Guilherme França, Karl Friston, Mark Girolami, Michael I. Jordan, Grigorios A. Pavliotis

A mixed generative model of auditory word repetition

Authors: Noor Sajid, Emma Holmes, Lancelot Da Costa, Cathy Price, Karl Friston

How Active Inference Could Help Revolutionise Robotics

Authors: Lancelot Da Costa, Pablo Lanillos, Noor Sajid, Karl Friston, Shujhat Khan

Universality of Winning Tickets: A Renormalization Group Perspective

Authors: William T. Redman, Tianlong Chen, Zhangyang Wang, Akshunna S. Dogra

Hamiltonian neural networks for solving equations of motion

Authors: Marios Mattheakis, David Sondak, Akshunna S. Dogra, Pavlos Protopapas

Axioms for Quantum Gauge Fields

Authors: Min Chul Lee, James Glimm

Simulation methods and error analysis for trawl processes and ambit fields

Authors: Dan Leonte, Almut E. D. Veraart

McKean-Vlasov Equations with Positive Feedback through Elastic Stopping Times

Authors: Ben Hambly, Julian Meier

SEC Form 13F-HR: Statistical investigation of trading imbalances and profitability analysis

Authors: Deborah Miori, Mihai Cucuringu

Returns-Driven Macro Regimes and Characteristic Lead-Lag Behaviour between Asset Classes

Authors: Deborah Miori, Mihai Cucuringu

Decentralised Finance and Automated Market Making: Execution and Speculation

Authors: Álvaro Cartea, Fayçal Drissi, Marcello Monga

Convergence and Implicit Regularization Properties of Gradient Descent for Deep Residual Networks

Authors: Rama Cont, Alain Rossier, RenYuan Xu

On the (Non-)Stationary Density of Fractional-Driven Stochastic Differential Equations

Authors: Xue-Mei Li, Fabien Panloup, Julian Sieber

Markov decision processes with observation costs

Authors: Christoph Reisinger, Jonathan Tam

Topologies on unparameterised path space

Authors: Thomas Cass, William F. Turner

Continuous-time stochastic gradient descent for optimizing over the stationary distribution of stochastic differential equations

Authors: Ziheng Wang, Justin Sirignano

Interactions of market making algorithms: a study on perceived collusion

Authors: Wei Xiong, Rama Cont

Random vortex dynamics via functional stochastic differential equations

Authors: Zhongmin Qian, Endre Süli, Yihuang Zhang

Volatility forecasting with machine learning and intraday commonality

Authors: Chao Zhang, Yihuang Zhang, Mihai Cucuringu, Zhongmin Qian


Existence and uniqueness of quasi-stationary and quasi-ergodic measures for absorbing Markov processes: a Banach lattice approach

Authors: Matheus M. Castro, Jeroen S. W. Lamb, Guillermo Olicón Méndez, Martin Rasmussen

The mean field limit of stochastic differential equation systems modelling grid cells

Authors: José A. Carrillo, Andrea Clini, Susanne Solem

Memory and Markov Blankets

Authors: Thomas Parr, Lancelot Da Costa, Conor Heins, Maxwell James D. Ramstead, Karl J. Friston

Stochastic Chaos and Markov Blankets

Authors: Karl Friston, Conor Heins, Kai Ueltzhöffer, Lancelot Da Costa, Thomas Parr

A Drive towards Thermodynamic Efficiency for Dissipative Structures in Chemical Reaction Networks

Authors: Kai Ueltzhöffer, Lancelot Da Costa, Daniela Cialfi, Karl Friston

Active inference, Bayesian optimal design, and expected utility

Authors: Noor Sajid, Lancelot Da Costa, Thomas Parr, Karl Friston

Branching Time Active Inference: the theory and its generality

Authors: Théophile Champion, Lancelot Da Costa, Howard Bowman, Marek Grześ

Bayesian brains and the Rényi divergence

Authors: Noor Sajid, Francesco Faccio, Lancelot Da Costa, Thomas Parr, Jürgen Schmidhuber, Karl Friston

Bayesian Mechanics for Stationary Processes

Authors: Lancelot Da Costa, Karl Friston, Conor Heins, Grigorios A. Pavliotis

Signature asymptotics, empirical processes, and optimal transport

Authors: Thomas Cass, Remy Messadene

The dynamics of the Koopman-van Hove angular and linear momentum operators

Authors: Remy Messadene

Closed-Loop Nash Competition for Liquidity

Authors: Alessandro Micheli, Johannes Muhle-Karbe, Eyal Neuman

Scaling Properties of Deep Residual Networks

Authors: Alain-Sam Cohen, Rama Cont, Alain Rossier, Renyuan Xu

Mild Stochastic Sewing Lemma, SPDE in Random Environment, and Fractional Averaging

Authors: Xue-Mei Li, Julian Sieber

Functional Limit Theorems for Volterra Processes and Applications to Homogenization

Authors: Johann Gehringer, Xue-Mei Li, Julian Sieber

Modelling SARS-CoV-2 coevolution with genetic algorithms

Authors: Aymeric Vie

Emergence of more contagious COVID-19 variants from the coevolution of viruses and policy interventions

Authors: Aymeric Vie 

Population network structure impacts genetic algorithm optimisation performance

Authors: Aymeric Vie

Global Convergence of the ODE Limit for Online Actor-Critic Algorithms in Reinforcement Learning

Authors: Ziheng Wang, Justin Sirignano

Universality for the directed configuration model with random degrees: metric space convergence of the strongly connected components at criticality

Authors: Serte Donderwinkel, Zheneng Xie

Tracking the vortex motion by using Brownian fluid particles

Authors: Zhongmin Qian, Youchun Qiu, Yihuang Zhang

Large and moderate deviations for importance sampling in the Heston model

Authors: Marc Geha, Antoine Jacquier, Zan Zuric

Deep Hedging under Rough Volatility

Authors: Blanka Horvath, Josef Teichmann, Zan Zuric


The relationship between dynamic programming and active inference: the discrete, finite-horizon case

Authors: Lancelot Da Costa, Noor Sajid, Thomas Parr, Karl Friston, Ryan Smith

Sophisticated Inference

Authors: Karl Friston, Lancelot Da Costa, Danijar Hafner, Casper Hesp, Thomas Parr

Some interesting observations on the free energy principle

Authors: Karl Friston, Lancelot Da Costa, Thomas Parr

Active inference on discrete state-spaces: a synthesis

Authors: Lancelot Da Costa, Thomas Parr, Noor Sajid, Sebastijan Veselic, Victorita Neacsu, Karl Friston

Evidence of Crowding on Russell 3000 Reconstitution Events

Authors: Alessandro Micheli, Eyal Neuman

Slow-Fast Systems with Fractional Environment and Dynamics

Authors: Xue-Mei Li, Julian Sieber

Formulae for the Derivative of the Poincaré Constant of Gibbs Measures

Authors: Julian Sieber

Qualities, challenges and future of genetic algorithms: a literature review

Authors: Aymeric Vie, Alissa M. Kleinnijenhuis, Doyne J. Farmer

Asymptotic strong Feller property and local weak irreducibility via generalized couplings

Authors: Oleg Butkovsky, Fabrice Wunderlich

Robust pricing and hedging via neural SDEs

Authors: Patryk Gierjatowicz, Marc Sabate-Vidales, David Šiška, Lukasz Szpruch, Žan Žurič



A typical realisation of the Brownian web: coalescing Brownian trajectories emanate from every point of the plane simultaneously. Trajectories are coloured according to their creation time/age. (Martin Hairer)


A simulation of Dyson Brownian motion for the Gaussian Orthogonal Ensemble of random symmetric matrices of size 50. (Jon Keating)