38 citations · 150 across the 39 of their papers we have counts for
3 papers · 1 filter
Cascade equation for the discontinuities in the Stefan problem with surface tension
Yucheng Guo, Sergey Nadtochiy, Mykhaylo Shkolnikov
The Stefan problem with surface tension is well known to exhibit discontinuities in the associated moving aggregate (i.e., in the domain occupied by the solid), whose structure has…
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.…
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…