Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOn Distribution depend SDEs with singular drifts
104
0
0.0
(
0
)
Authors
Guohuan Zhao
Ask ChatGPT about the research
No Arabic abstract
We investigate the well-posedness of distribution dependent SDEs with singular coefficients. Existence is proved when the diffusion coefficient satisfies some non-degeneracy and mild regularity assumptions, and the drift coefficient satisfies an integrability condition and a continuity condition with respect to the (generalized) total variation distance. Uniqueness is also obtained under some additional Lipschitz type continuity assumptions.
rate research
Read More
In this paper, utilizing Wangs Harnack inequality with power and the Banach fixed point theorem, the weak well-posedness for distribution dependent SDEs with integrable drift is investigated. In addition, using a trick of decoupled method, some regularity such as relative entropy and Sobolevs estimate of invariant probability measure are proved. Furthermore, by comparing two stationary Fokker-Planck-Kolmogorov equations, the existence and uniqueness of invariant probability measure for McKean-Vlasov SDEs are obtained by log-Sobolevs inequality and Banachs fixed theorem. Finally, some examples are presented.
We obtain $T_2(C)$ for stochastic differential equations with Dini continuous drift and $T_1(C)$ stochastic differential equations with singular coefficients.
In this paper, we study (strong and weak) existence and uniqueness of a class of non-Markovian SDEs whose drift contains the derivative in the sense of distributionsof a continuous function.
We prove the unique weak solvability of time-inhomogeneous stochastic differential equations with additive noises and drifts in critical Lebsgue space $L^q([0,T]; L^{p}(mathbb{R}^d))$ with $d/p+2/q=1$. The weak uniqueness is obtained by solving corresponding Kolmogorovs backward equations in some second order Sobolev spaces, which is analytically interesting in itself.
The paper investigates existence and uniqueness for a stochastic differential equation (SDE) with distributional drift depending on the law density of the solution. Those equations are known as McKean SDEs. The McKean SDE is interpreted in the sense of a suitable singular martingale problem. A key tool used in the investigation is the study of the corresponding Fokker-Planck equation.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
