Convergence of Random Walks towards Skew Brownian motion

13.06.2022, 13:00  –  Haus 9, Raum 2.22
Forschungsseminar Wahrscheinlichkeitstheorie

Andrey Pilipenko (Acad. of Science, Kyiv)

We consider the random motion of a particle, whose jumps outside of a bounded set (membrane) are mean-zero i.i.d.  with a finite second moment. Jumps from the membrane have other finite mean distributions which may be different at different points ; they are also mutually independent and independent of the jumps outside the membrane.

We prove that Donsker's scaling limit of this random walk is a skew Brownian motion, i.e., a diffusion with a unit diffusion coefficient and a degenerate drift equal to  a δ_0, where |a| ≤1.

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