Abstract
AbstractWe consider the stochastic differential equation dXt = A(Xt−)dZt, X0 = x, driven by cylindrical α-stable process Zt in , where α ∈ (0,1) and d ≥ 2. We assume that the determinant of A(x) = (aij(x)) is bounded away from zero, and aij(x) are bounded and Lipschitz continuous. We show that for any fixed γ ∈ (0,α) the semigroup Pt of the process Xt satisfies $|P_{t} f(x) - P_{t} f(y)| \le c t^{-\gamma /\alpha } |x - y|^{\gamma } ||f||_{\infty }$
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for arbitrary bounded Borel function f. Our approach is based on Levi’s method.
Publisher
Springer Science and Business Media LLC
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