38 citations · 150 across the 39 of their papers we have counts for
48 papers
Universal Central Limit Theorem for non-exchangeable interacting diffusions
Mykhaylo Shkolnikov, Lane Chun Yeung
We study non-exchangeable interacting diffusions with pairwise interaction strengths encoded by a sequence of matrices. Under suitable structural and denseness conditions on these…
Relative arbitrage problem under eigenvalue lower bounds
Jou-Hua Lai, Mykhaylo Shkolnikov, H. Mete Soner
We give a new formulation of the relative arbitrage problem from stochastic portfolio theory that asks for a time horizon beyond which arbitrage relative to the market exists in al…
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…
Deep Level-set Method for Stefan Problems
Mykhaylo Shkolnikov, H. Mete Soner, Valentin Tissot-Daguette
We propose a level-set approach to characterize the region occupied by the solid in Stefan problems with and without surface tension, based on their recent probabilistic reformulat…