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SUMMARY:Lecture 1 (July 30). Generalized Skorokhod’s reflecting problem.
  - Andrey Pilipenko (National Academy of Sciences of Ukraine)
DTSTART:20240730T090000Z
DTEND:20240730T100000Z
UID:TALK218698@talks.cam.ac.uk
DESCRIPTION:The Skorokhod reflection was used in 1961 to create a reflecte
 d diffusion on the half-line. Later\, it was used for processes with jumps
  such as reflected L&eacute\;vy processes. Like a Brownian motion\, which 
 is a weak limit of random walks\, reflected processes on the half-line ser
 ve as weak limits of random walks with switching regimes at zero: one regi
 me away from zero\, the other around zero. We develop a general theory of 
 this regime change and prove convergence to a function with generalized re
 flection. Our results are deterministic and can be applied to a wide class
  of stochastic processes. Applications include storage processes\, heavy t
 raffic limits\, diffusion on a half-line with a combination of continuous 
 reflection\, jump exit\, and a delay at 0.
LOCATION:Seminar Room 2\, Newton Institute
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