157 citations · 632 across the 40 of their papers we have counts for
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Strong solutions of stochastic equations with rank-based coefficients
Tomoyuki Ichiba, Ioannis Karatzas, Mykhaylo Shkolnikov
We study finite and countably infinite systems of stochastic differential equations, in which the drift and diffusion coefficients of each component (particle) are determined by it…
On the one-sided Tanaka equation with drift
Ioannis Karatzas, Albert N. Shiryaev, Mykhaylo Shkolnikov
We study questions of existence and uniqueness of weak and strong solutions for a one-sided Tanaka equation with constant drift λ. We observe a dichotomy in terms of the values of…
Planar Diffusions with Rank-Based Characteristics: Transition Probabilities, Time Reversal, Maximality and Perturbed Tanaka equations
E. Robert Fernholz, Tomoyuki Ichiba, Ioannis Karatzas +1
We construct a planar diffusion process whose infinitesimal generator depends only on the order of the components of the process. Speaking informally and a bit imprecisely for the…