38 citations · 150 across the 39 of their papers we have counts for
7 papers · 2 filters
Fluctuations of Martingales and Winning Probabilities of Game Contestants
David Aldous, Mykhaylo Shkolnikov
Within a contest there is some probability M_i(t) that contestant i will be the winner, given information available at time t, and M_i(t) must be a martingale in t. Assume continuo…
Large deviations for diffusions interacting through their ranks
Amir Dembo, Mykhaylo Shkolnikov, S. R. Srinivasa Varadhan +1
We prove a Large Deviations Principle (LDP) for systems of diffusions (particles) interacting through their ranks, when the number of particles tends to infinity. We show that the…
Systems of Brownian particles with asymmetric collisions
Ioannis Karatzas, Soumik Pal, Mykhaylo Shkolnikov
We study systems of Brownian particles on the real line, which interact by splitting the local times of collisions among themselves in an asymmetric manner. We prove the strong exi…
Small time central limit theorems for semimartingales with applications
Stefan Gerhold, Max Kleinert, Piet Porkert +1
We give conditions under which the normalized marginal distribution of a semimartingale converges to a Gaussian limit law as time tends to zero. In particular, our result is applic…
Limits of Multilevel TASEP and similar processes
Vadim Gorin, Mykhaylo Shkolnikov
We study the asymptotic behavior of a class of stochastic dynamics on interlacing particle configurations (also known as Gelfand-Tsetlin patterns). Examples of such dynamics includ…
On a non-linear transformation between Brownian martingales
Mykhaylo Shkolnikov
The paper studies a non-linear transformation between Brownian martingales, which is given by the inverse of the pricing operator in the mathematical finance terminology. Subsequen…