38 citations · 44 across the 17 of their papers we have counts for
7 papers · 1 filter
Stefan problem with surface tension: global existence of physical solutions under radial symmetry
Sergey Nadtochiy, Mykhaylo Shkolnikov
We consider the Stefan problem with surface tension, also known as the Stefan-Gibbs-Thomson problem, in an ambient space of arbitrary dimension. Assuming the radial symmetry of the…
Scaling limits of external multi-particle DLA on the plane and the supercooled Stefan problem
Sergey Nadtochiy, Mykhaylo Shkolnikov, Xiling Zhang
We consider (a variant of) the external multi-particle diffusion-limited aggregation (MDLA) process of Rosenstock and Marquardt on the plane. Based on the recent findings of [11],…
Reflected BSDEs in non-convex domains
Jean-François Chassagneux, Sergey Nadtochiy, Adrien Richou
This paper establishes the well-posedness of reflected backward stochastic differential equations in the non-convex domains that satisfy a weaker version of the star-shaped propert…
Global solutions to the supercooled Stefan problem with blow-ups: regularity and uniqueness
Francois Delarue, Sergey Nadtochiy, Mykhaylo Shkolnikov
We consider the supercooled Stefan problem, which captures the freezing of a supercooled liquid, in one space dimension. A probabilistic reformulation of the problem allows to defi…
Mean field systems on networks, with singular interaction through hitting times
Sergey Nadtochiy, Mykhaylo Shkolnikov
Building on the line of work [DIRT15a], [DIRT15b], [NS17a], [DT17], [HLS18], [HS18] we continue the study of particle systems with singular interaction through hitting times. In co…
Particle systems with singular interaction through hitting times: application in systemic risk modeling
Sergey Nadtochiy, Mykhaylo Shkolnikov
We propose an interacting particle system to model the evolution of a system of banks with mutual exposures. In this model, a bank defaults when its normalized asset value hits a l…
Weak reflection principle for Lévy processes
Erhan Bayraktar, Sergey Nadtochiy
In this paper, we develop a new mathematical technique which allows us to express the joint distribution of a Markov process and its running maximum (or minimum) through the margin…