• Corpus ID: 251564190

Drift reduction method for SDEs driven by inhomogeneous singular L{\'e}vy noise

  title={Drift reduction method for SDEs driven by inhomogeneous singular L\{\'e\}vy noise},
  author={Tadeusz Kulczycki and Oleksii Kulyk and Michał Ryznar},
. We study SDE where Z = ( Z 1 ,...,Z d ) T , with Z i ,i = 1 ,...,d being independent one-dimensional symmetric jump L´evy processes, not necessarily identically distributed. In par- ticular, we cover the case when each Z i is one-dimensional symmetric α i -stable process ( α i ∈ (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… 



Supercritical SDEs driven by multiplicative stable-like Lévy processes

In this paper, we study the following time-dependent stochastic differential equation (SDE) in Rd: dXt = σ(t,Xt−)dZt + b(t,Xt)dt, X0 = x ∈ R, where Z is a d-dimensional non-degenerate α-stable-like

On weak solution of SDE driven by inhomogeneous singular Lévy noise

We study a time-inhomogeneous SDE in R driven by a cylindrical Lévy process with independent coordinates which may have different scaling properties. Such a structure of the driving noise makes it

On weak uniqueness and distributional properties of a solution to an SDE with α-stable noise

  • A. Kulik
  • Mathematics
    Stochastic Processes and their Applications
  • 2019

The martingale problem for anisotropic nonlocal operators

We consider systems of stochastic differential equations of the form \[ d X_t^i = \sum_{j=1}^d A_{ij}(X_{t-}) d Z_t^j\] for $i=1,\dots,d$ with continuous, bounded and non-degenerate coefficients.

Construction and heat kernel estimates of general stable-like Markov processes

A stable-like process is a Feller process $(X_t)_{t\geq 0}$ taking values in $\mathbb{R}^d$ and whose generator behaves, locally, like an $\alpha$-stable Levy process, but the index $\alpha$ and all

Semigroup properties of solutions of SDEs driven by Lévy processes with independent coordinates

Parametrix construction of the transition probability density of the solution to an SDE driven by $\alpha$-stable noise

Let $L:= -a(x) (-\Delta)^{\alpha/2}+ (b(x), \nabla)$, where $\alpha\in (0,2)$, and $a:\rd\to (0,\infty)$, $b: \rd\to \rd$. Under certain regularity assumptions on the coefficients $a$ and $b$, we

Regularity of solutions to anisotropic nonlocal equations

We study harmonic functions associated to systems of stochastic differential equations of the form $$dX_t^i=A_{i1}(X_{t-})dZ_t^1+\cdots +A_{id}(X_{t-})dZ_t^d$$ d X t i = A i 1 ( X t - ) d Z t 1 + ⋯ +

Existence of densities for stochastic differential equations driven by Lévy processes with anisotropic jumps

We study existence of densities for solutions to stochastic differential equations with Holder continuous coefficients and driven by a $d$-dimensional Levy process $Z=(Z_{t})_{t\geq 0}$, where, for