اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدOn Distribution depend SDEs with singular drifts
104
0
0.0
(
0
)
تأليف
Guohuan Zhao
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
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.
قيم البحث
اقرأ أيضاً
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 regul
arity 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 corre
sponding 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.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
