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

@inproceedings{Kulczycki2022DriftRM, title={Drift reduction method for SDEs driven by inhomogeneous singular L\{\'e\}vy noise}, author={Tadeusz Kulczycki and Oleksii Kulyk and Michał Ryznar}, year={2022} }

. 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…

## References

SHOWING 1-10 OF 18 REFERENCES

### Supercritical SDEs driven by multiplicative stable-like Lévy processes

- MathematicsTransactions of the American Mathematical Society
- 2021

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

- Mathematics
- 2021

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

- MathematicsStochastic Processes and their Applications
- 2019

### The martingale problem for anisotropic nonlocal operators

- Mathematics
- 2018

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

- MathematicsDissertationes Mathematicae
- 2021

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

- MathematicsStochastic Processes and their Applications
- 2020

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

- Mathematics
- 2014

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

- MathematicsMathematische Zeitschrift
- 2020

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

- MathematicsAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques
- 2021

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…