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Systems of rough stochastic differential equations I: weak existence and Yamada--Watanabe
Florian Huber
For systems of rough stochastic differential equations in the sense of Friz--Hocquet--Lê, with a fixed deterministic rough driver, we prove two results. The first is weak existence…
Fluctuation Correction and Global Solutions for the Stochastic Shigesada-Kawasaki-Teramoto System via Entropy-Based Regularization
Florian Huber
We study a stochastic extension of the n-species Shigesada-Kawasaki-Teramoto (SKT) cross-diffusion system, in which a multiplicative noise term accounts for fluctuation corrections…
Markovian Lifts of Stochastic Volterra Equations in Sobolev Spaces: Solution theory, an Ito Formula and Invariant Measures
Florian Huber
We investigate Markovian lifts of stochastic Volterra equations (SVEs) with completely monotone kernels and general coefficients within the framework of weighted Sobolev spaces. Ou…
Polynomial interacting particle systems and non-linear SPDEs for market capitalization curves
Christa Cuchiero, Florian Huber
Motivated by the robustness of the capital distribution curves, we study the behavior of a certain polynomial equity market model as the number of companies goes to infinity. More…