19 citations · 52 across the 21 of their papers we have counts for
17 papers · 1 filter
Probabilistic estimates for a system of noisy integrate-and-fire neurons
Ben Hambly, Aldaïr Petronilia, Christoph Reisinger +1
In this note, we establish various probabilistic estimates for an interacting particle system that describes the evolution of the membrane potentials in a network of excitatory int…
Volterra clocks and their pure-jump limits: hitting times of curved boundaries
Eduardo Abi Jaber, Elie Attal, Andreas Sojmark
We introduce a class of continuous Volterra processes, called Volterra clocks, and study their singular limit as the memory kernel collapses to a Dirac mass at zero. The dynamics a…
A free boundary problem for the mean-field limit of diffusing particles with nonlinear boundary reactivity
Eliana Fausti, Andreas Sojmark
Consider a finite system of diffusing particles coupled through a reactive boundary. Each particle is reflected, but may react with the boundary according to a killing mechanism wh…
A Moving Boundary Problem for Brownian Particles with Singular Forward-Backward Interactions
Philipp Jettkant, Andreas Sojmark
We introduce a system of Brownian particles, each absorbed upon hitting an associated moving boundary. The boundaries are determined by the conditional probabilities of the particl…
The supercooled Stefan problem with transport noise: weak solutions and blow-up
Sean Ledger, Andreas Sojmark
We derive two weak formulations for the supercooled Stefan problem with transport noise on a half-line: one captures a continuously evolving system, while the other resolves blow-u…
Functional CLTs for subordinated Lévy models in physics, finance, and econometrics
Andreas Søjmark, Fabrice Wunderlich
We present a simple unifying treatment of a broad class of applications from statistical mechanics, econometrics, mathematical finance, and insurance mathematics, where (possibly s…
Functional weak convergence of stochastic integrals for moving averages and continuous-time random walks
Andreas Søjmark, Fabrice Wunderlich
There is an extensive theory of weak convergence for moving averages and continuous-time random walks (CTRWs) with respect to Skorokhod's M1 and J1 topologies. Here we address the…
Weak Convergence of Stochastic Integrals on Skorokhod Space in Skorokhod's J1 and M1 Topologies
Andreas Sojmark, Fabrice Wunderlich
We provide criteria for Itô integration to behave continuously with respect to Skorokhod's J1 and M1 topologies, when the integrands and integrators converge weakly or in probabili…
Contagious McKean--Vlasov problems with common noise: from smooth to singular feedback through hitting times
Ben Hambly, Aldaïr Petronilia, Christoph Reisinger +2
We consider a family of McKean--Vlasov equations arising as the large particle limit of a system of interacting particles on the positive half-line with common noise and feedback.…
An SPDE with Robin-type boundary for a system of elastically killed diffusions on the positive half-line
Ben Hambly, Julian Meier, Andreas Sojmark
We consider a system of particles undergoing correlated diffusion with elastic boundary conditions on the half-line. By taking the large particle limit we establish existence and u…
An interacting particle system for the front of an epidemic advancing through a susceptible population
Eliana Fausti, Andreas Sojmark
We introduce an interacting particle system that models the spread of an epidemic in terms of heterogeneous diffusive dynamics, rather than exogenous contact and transmission rates…
Contagious McKean-Vlasov systems with heterogeneous impact and exposure
Zachary Feinstein, Andreas Sojmark
We introduce a heterogeneous formulation of a contagious McKean-Vlasov system, whose inherent heterogeneity comes from asymmetric interactions with a natural and highly tractable s…
Uniqueness for contagious McKean--Vlasov systems in the weak feedback regime
Sean Ledger, Andreas Sojmark
We present a simple uniqueness argument for a collection of McKean-Vlasov problems that have seen recent interest. Our first result shows that, in the weak feedback regime, there i…
At the Mercy of the Common Noise: Blow-ups in a Conditional McKean--Vlasov Problem
Sean Ledger, Andreas Sojmark
We extend a model of positive feedback and contagion in large mean-field systems, by introducing a common source of noise driven by Brownian motion. Although the driving dynamics a…
An SPDE Model for Systemic Risk with Endogenous Contagion
Ben Hambly, Andreas Sojmark
We propose a dynamic mean field model for `systemic risk' in large financial systems, which we derive from a system of interacting diffusions on the positive half-line with an abso…
A McKean--Vlasov equation with positive feedback and blow-ups
Ben Hambly, Sean Ledger, Andreas Sojmark
We study a McKean--Vlasov equation arising from a mean-field model of a particle system with positive feedback. As particles hit a barrier they cause the other particles to jump in…
Functional central limit theorems for rough volatility
Blanka Horvath, Antoine Jacquier, Aitor Muguruza +1
The non-Markovian nature of rough volatility processes makes Monte Carlo methods challenging and it is in fact a major challenge to develop fast and accurate simulation algorithms.…