10 papers
An Additive-Noise Approximation to Keller-Segel-Dean-Kawasaki Dynamics: Small-Noise Results
Adrian Martini, Avi Mayorcas
We study an additive-noise approximation to Keller-Segel-Dean-Kawasaki dynamics, which is proposed as an approximate model to the fluctuating hydrodynamics of chemotactically inter…
Quantitative Propagation of Chaos for Singular Interacting Particle Systems Driven by Fractional Brownian Motion
Lucio Galeati, Khoa Lê, Avi Mayorcas
We consider interacting systems particle driven by i.i.d. fractional Brownian motions, subject to irregular, possibly distributional, pairwise interactions. We show propagation of…
Ergodic Theory for Fractional SDE with Singular Coefficients
Avi Mayorcas, Åukasz MÄ dry
We show existence and uniqueness of invariant measures for SDE of the form \[ dX_t = g(X_t)dt + u(X_t)dt + dW^H_t \] where is a fractional Brownian motion (fBm) with Hurst pa…
Homogenisation of a Passive Scalar Transported by Locally Supported White Noise
Federico Butori, Avi Mayorcas, Silvia Morlacchi
Stochastic perturbations of transport type are a common and widely accepted way of representing turbulent effects in fluid dynamics models. In many known examples, it even leads to…
Stochastic Analysis of Overlapping Generations Models Under Incomplete Markets
Cangxiong Chen, Sigmund Ellingsrud, Fabian Harang +2
We provide a stochastic analysis of an overlapping-generations model under incomplete markets. By casting individual optimisation with idiosyncratic income risk into a forward-back…
Introduction to SPDEs from Probability and PDE
Avi Mayorcas
Lecture notes accompanying an 8hr hour mini-course on SPDE given at BoÄaziçi University, Istanbul in June/July 2025. They are based on earlier notes of a shorter mini-course give…