4 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…
Intertwining diffusions and wave equations
Benjamin Budway, Soumik Pal, Mykhaylo Shkolnikov
We develop a general theory of intertwined diffusion processes of any dimension. Our main result gives an SDE construction of intertwinings of diffusion processes and shows that th…
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…