Andrey Pilipenko (Nat. Acad. of Sciences & Nat. TU of Ukraine, Kyiv)
The Skorokhod reflection was used in 1961 to create a reflected Brownian motion on the half-line. Later, it was used for processes with jumps such as reflected Lévy processes. Like a Brownian motion, which is a weak limit of random walks, reflected processes on the half-line serve as weak limits of random walks with switching regimes at zero: one regime away from zero, the other around zero. We develop a general theory of this regime change and prove convergence to a function with generalized reflection. Our results are deterministic but can be applied to a wide class of stochastic processes. Applications include storage processes, heavy traffic limits, diffusion on a half-line with a combination of continuous reflection, jump exit and a delay at 0.
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