POINTWISE WEAK EXISTENCE OF DISTORTED SKEW BROWNIAN MOTION WITH RESPECT TO DISCONTINUOUS MUCKENHOUPT WEIGHTS

For any starting point in R-d, d >= 3, we identify the stochastic differential equation of distorted Brownian motion with respect to a certain discontinuous Muckenhoupt A(2)-weigh psi. The discontinuities of psi typically take place on a sequence of level sets of the Euclidean norm D-k := {x is an element of R-d vertical bar parallel to x parallel to = d(k) }, k is an element of Z, where (d(k)) (k is an element of Z) subset of (0, infinity) may have accumulation points and each level set D-k plays the role of a permeable membrane.