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math.PR2024
From rank-based models with common noise to pathwise entropy solutions of SPDEs
Mykhaylo Shkolnikov, Lane Chun Yeung
We study the mean field limit of a rank-based model with common noise, which arises as an extension to models for the market capitalization of firms in stochastic portfolio theory.…
math.PR2024
Multilevel Dyson Brownian motions via the superposition principle
Benjamin Budway, Mykhaylo Shkolnikov
Multilevel Dyson Brownian motions (MDBMs) combine Dyson Brownian motions of different dimensions into a single process in a canonical way. This paper completes the theory of MDBMs…