论文标题
由不均匀的单数l {é} vy噪声驱动的SDE的漂移减少方法
Drift reduction method for SDEs driven by inhomogeneous singular L{é}vy noise
论文作者
论文摘要
我们研究sde $$ d x_t = b（x_t）\，dt + a（x_ {t-}）\，d z_t，\ quad x_ {0} = x \ in \ in \ in \ mathbb {r}^d，\ quad quad t \ quad t \ geq 0 $ z =（ i = 1，\ dots，d $是独立的一维对称跳跃过程，不一定是分布的。特别是，当每个$ z^i $都是一维对称$α_i$稳定过程（$α_i\ in（0,2）$，它们不一定是相等的）。 根据$ b $，$ a $和$ z $的某些假设，我们表明，SDE的弱解决方案是唯一定义的，Markov，我们提供了过渡概率密度的表示，并建立了相应的过渡半群的h {Ö} lder规律性。 我们提出的方法是基于将漂移项的SDE降低到另一个SDE，而没有这样的术语，但取决于时间变量的系数。这种方法具有经典特征方法具有相同的精神，并且似乎具有独立的兴趣。
We study SDE $$ d X_t = b(X_t) \, dt + A(X_{t-}) \, d Z_t, \quad X_{0} = x \in \mathbb{R}^d, \quad t \geq 0 $$ where $Z=(Z^1, \dots, Z^d)^T$, with $Z^i, i=1,\dots, d$ being independent one-dimensional symmetric jump Lévy processes, not necessarily identically distributed. In particular, we cover the case when each $Z^i$ is one-dimensional symmetric $α_i$-stable process ($α_i \in (0,2)$ and they are not necessarily equal). Under certain assumptions on $b$, $A$ and $Z$ we show that the weak solution to the SDE is uniquely defined and Markov, we provide a representation of the transition probability density and we establish H{ö}lder regularity of the corresponding transition semigroup. The method we propose is based on a reduction of an SDE with a drift term to another SDE without such a term but with coefficients depending on time variable. Such a method have the same spirit with the classic characteristic method and seems to be of independent interest.
