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- W2895930635 abstract "We study existence of densities for solutions to stochastic differential equations with Holder continuous coefficients and driven by a $d$-dimensional Levy process $Z=(Z_{t})_{tgeq 0}$, where, for $t>0$, the density function $f_{t}$ of $Z_{t}$ exists and satisfies, for some $(alpha_{i})_{i=1,dots,d}subset(0,2)$ and $C>0$, begin{align*} limsuplimits _{t to 0}t^{1/alpha_{i}}intlimits _{mathbb{R}^{d}}|f_{t}(z+e_{i}h)-f_{t}(z)|dzleq C|h|, hin mathbb{R}, i=1,dots,d. end{align*} Here $e_{1},dots,e_{d}$ denote the canonical basis vectors in $mathbb{R}^{d}$. The latter condition covers anisotropic $(alpha_{1},dots,alpha_{d})$-stable laws but also particular cases of subordinate Brownian motion. To prove our result we use some ideas taken from citep{DF13}." @default.
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- W2895930635 date "2018-10-17" @default.
- W2895930635 modified "2023-09-27" @default.
- W2895930635 title "Existence of densities for stochastic differential equations driven by L'evy processes with anisotropic jumps" @default.
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