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