Summary
LetB=(B t,t≧0) be a planar Brownian motion and let α>0. For anyt≧0, the pointz=B t is called a one-sided cone point with angle α if there exist ε>0 and a wedgeW(α,z) with vertexz and angle α such thatB s∈W(α,z) for everys∈[t, t+ε]. Burdzy and Shimura have shown independently that one-sided cone points with angle α exist when α>π/2 but not when α<π/2. The present paper deals with the critical case α=π/2. We show that cone points with angle π/2 do not exist.
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Le Gall, J.F., Meyre, T. Points cônes du mouvement brownien plan, le cas critique. Probab. Th. Rel. Fields 93, 231–247 (1992). https://doi.org/10.1007/BF01195230
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DOI: https://doi.org/10.1007/BF01195230