We consider the stochastic differential equation dX_t = A(X_t−)dZ_t, X₀ = x, driven by cylindrical α-stable process Z_t in , where α ∈ (0,1) and d ≥ 2. We assume that the determinant of A(x) = (a_ij(x)) is bounded away from zero, and a_ij(x) are bounded and Lipschitz continuous. We show that for any fixed γ ∈ (0,α) the semigroup P_t of the process X_t satisfies \(|P_{t} f(x) - P_{t} f(y)| \le c t^{-\gamma /\alpha } |x - y|^{\gamma } ||f||_{\infty }\) for arbitrary bounded Borel function f. Our approach is based on Levi’s method.

中文翻译：

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乘性圆柱稳定噪声驱动的SDE具有强大的Feller特性

我们认为，随机微分方程d X_吨=甲（X_吨- ）d Ž_吨，X ₀ = X，由圆筒状的驱动α -stable过程Ž_吨中，其中α＆Element;（0,1）和d ≥2.我们假设A（x）=（a _{i j}（x））的行列式有界于零，而a _{i j}（x）有界且Lipschitz连续。我们表明，对于任何固定的γ＆Element;（0，α）的半群P_吨的处理的X_吨满足\（| P_ {吨} F（X） - P_ {吨} F（Y）| \文件克拉^ { - \ gamma / \ alpha} | x-y | ^ {\ gamma} || f || _ {\ infty} \）对于任意有界Borel函数f。我们的方法基于李维斯方法。