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math.PR2026
Sticky CIR process with potential: invariant measure and exact sampling
Tony Shardlow
We study the sticky Cox--Ingersoll--Ross (CIR) process in one dimension, a diffusion on with a sticky boundary condition at the origin, arising as the marginal process…
math.PR2018
From weakly interacting particles to a regularised Dean--Kawasaki model
Federico Cornalba, Tony Shardlow, Johannes Zimmer
The evolution of finitely many particles obeying Langevin dynamics is described by Dean-Kawasaki equations, a class of stochastic equations featuring a non-Lipschitz multiplicative…
math.PR2018★ 1 cited
A regularised Dean-Kawasaki model: derivation and analysis
Federico Cornalba, Tony Shardlow, Johannes Zimmer
The Dean-Kawasaki model consists of a nonlinear stochastic partial differential equation featuring a conservative, multiplicative, stochastic term with non-Lipschitz coefficient, a…