Sayed Anwar Elsaid Mohammed

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dXt = b(t,Xt) dt + dBt, s, t ∈ R, Xs = x ∈ R. The above SDE is driven by a bounded measurable drift coefficient b : R × Rd → Rd and a d-dimensional Brownian motion B. More specifically, we show that the stochastic flow φs,t(·) of the SDE lives in the space L2(Ω;W 1,p(Rd, w)) for all s, t and all p > 1, where W 1,p(Rd, w) denotes a weighted Sobolev space(More)
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