We study the stochastic differential equation $dX_t = A_t(X_{t-}) \, dZ_t$, $ X_0 = x$, where $Z_t = (Z_t^{(1)},\ldots,Z_t^{(d)})^T$ and for each $i \in \{1,\ldots,d\}$ $Z_t^{(i)}$ is a one-dimensional, symmetric $\alpha_i$-stable process, where $\alpha_i \in (0,2)$. Under appropriate conditions on $\alpha_1,\ldots,\alpha_d$ and on matrices $A_t$ we prove existence and uniqueness of the weak solution of the above SDE, which will be shown to be a time-inhomogeneous Markov process. We also provide a representation of the transition probability density of this process as a sum of explicitly given principal part, and a residual part subject to a set of estimates showing that this part is negligible in a short time. The talk is based on a joint work with A. Kulik and M. Ryznar, On weak solution of SDE driven by inhomogeneous singular Lévy noise, Trans. Amer. Math. Soc. (to appear).

Meeting ID: 251 152 4038 Passcode: 276466