Zobrazeno 1 - 10
of 146
pro vyhledávání: '"Shkolnikov, Mykhaylo"'
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 only been understood under translational or radial symmetry so far. I
Externí odkaz:
http://arxiv.org/abs/2410.15249
Autor:
Shkolnikov, Mykhaylo, Yeung, Lane Chun
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. We show that, under certain conditions on the drift and diffusion coe
Externí odkaz:
http://arxiv.org/abs/2406.07286
Autor:
Budway, Benjamin, Shkolnikov, Mykhaylo
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 for $\beta\ge2$. Specifically, we use the superposition principle of F
Externí odkaz:
http://arxiv.org/abs/2403.10724
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 reformulation. The level-set function is parameterized by a feed-forward neural
Externí odkaz:
http://arxiv.org/abs/2306.11601
We study the Stefan problem with surface tension and radially symmetric initial data. In this context, the notion of a so-called physical solution, which exists globally despite the inherent blow-ups of the melting rate, has been recently introduced
Externí odkaz:
http://arxiv.org/abs/2306.02969
We study the one-phase one-dimensional supercooled Stefan problem with oscillatory initial conditions. In this context, the global existence of so-called physical solutions has been shown recently in [CRSF20], despite the presence of blow-ups in the
Externí odkaz:
http://arxiv.org/abs/2302.13097
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 initial data we introduce a novel "probabilistic" notion of solution,
Externí odkaz:
http://arxiv.org/abs/2203.15113
Autor:
Baker, Graeme, Shkolnikov, Mykhaylo
We consider a probabilistic formulation of a singular two-phase Stefan problem in one space dimension, which amounts to a coupled system of two McKean-Vlasov stochastic differential equations. In the financial context of systemic risk, this system mo
Externí odkaz:
http://arxiv.org/abs/2203.06003
Publikováno v:
In Journal of Computational Physics 15 April 2024 503
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], [10] in one space dimension it is natural to conjecture that the scali
Externí odkaz:
http://arxiv.org/abs/2102.09040