38 citations · 150 across the 39 of their papers we have counts for
4 papers · 1 filter
Time-reversal of reflected Brownian motions in the orthant
Mykhaylo Shkolnikov, Ioannis Karatzas
We determine the processes obtained from a large class of reflected Brownian motions (RBMs) in the nonnegative orthant by means of time reversal. The class of RBMs we deal with inc…
Intertwining diffusions and wave equations
Benjamin Budway, Soumik Pal, Mykhaylo Shkolnikov
We develop a general theory of intertwined diffusion processes of any dimension. Our main result gives an SDE construction of intertwinings of diffusion processes and shows that th…
Large deviations for interacting Bessel-like processes and applications to systemic risk
Tomoyuki Ichiba, Mykhaylo Shkolnikov
We establish a process level large deviation principle for systems of interacting Bessel-like diffusion processes. By establishing weak uniqueness for the limiting non-local SDE of…
Multidimensional sticky Brownian motions as limits of exclusion processes
Miklós Z. Rácz, Mykhaylo Shkolnikov
We study exclusion processes on the integer lattice in which particles change their velocities due to stickiness. Specifically, whenever two or more particles occupy adjacent sites…