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math.PR2012★ 1 cited
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…
math.PR2010★ 2 cited
Large systems of diffusions interacting through their ranks
Mykhaylo Shkolnikov
We study the limiting behaviour of the empirical measure of a system of diffusions interacting through their ranks when the number of diffusions tends to infinity. We prove that th…