1 citations · 1 across the 3 of their papers we have counts for
4 papers
Existence theorems for nonlinear stationary Kolmogorov equations with partially degenerate diffusion matrices
Aziz M. Embarek, Dmitry V. Shatilovich
We study nonlinear stationary Kolmogorov equations with degenerate diffusion matrices and discontinuous coefficients. The existence of a solution is proved. We propose a new approa…
Doubling variables and uniqueness of probability solutions to degenerate stationary Kolmogorov equations
V. I. Bogachev, S. V. Shaposhnikov, D. V. Shatilovich
We obtain sufficient conditions for the uniqueness of a probability solution to the stationary Kolmogorov equation with a degenerate diffusion matrix. We employ the method of doubl…
Analysis of mean field games via Fokker-Planck-Kolmogorov equations: existence of equilibria
Stanislav V. Shaposhnikov, Dmitry V. Shatilovich
We study mean field games with unbounded coefficients. The existence of a solution is proved. We propose a new approach based on Fokker-Planck-Kolmogorov equations, the Ambrosio-Fi…
On convergence of forecasts in prediction markets
Nina Badulina, Dmitry Shatilovich, Mikhail Zhitlukhin
We propose a dynamic model of a prediction market in which agents predict the values of a sequence of random vectors. The main result shows that if there are agents who make correc…