Lecture 1 (July 30). Generalized Skorokhod’s reflecting problem.

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• Andrey Pilipenko (National Academy of Sciences of Ukraine)
• Tuesday 30 July 2024, 10:00-11:00
• Seminar Room 2, Newton Institute.

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SSD - Stochastic systems for anomalous diffusion

The Skorokhod reflection was used in 1961 to create a reflected diffusion 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 and 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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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