اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدWong-Zakai Approximation for SDEs Driven by $G-$Brownian Motion
129
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In this paper, we build the equivalence between rough differential equations driven by the lifted $G$-Brownian motion and the corresponding Stratonovich type SDE through the Wong-Zakai approximation. The quasi-surely convergence rate of Wong-Zakai approximation to $G-$SDEs with mesh-size $frac{1}{n}$ in the $alpha$-Holder norm is estimated as $(frac{1}{n})^{frac12-}.$ As corollary, we obtain the quasi-surely continuity of the above RDEs with respect to uniform norm.
قيم البحث
اقرأ أيضاً
Sufficient and necessary conditions are presented for the comparison theorem of path dependent $G$-SDEs. Different from the corresponding study in path independent $G$-SDEs, a probability method is applied to prove these results. Moreover, the results extend the ones in the linear expectation case.
We establish Harnack inequality and shift Harnack inequality for stochastic differential equation driven by $G$-Brownian motion. As applications, the uniqueness of invariant linear expectations and estimates on the $sup$-kernel are investigated, wher
e the $sup$-kernel is introduced in this paper for the first time.
This paper is devoted to studying the properties of the exit times of stochastic differential equations driven by $G$-Brownian motion ($G$-SDEs). In particular, we prove that the exit times of $G$-SDEs has the quasi-continuity property. As an applica
tion, we give a probabilistic representation for a large class of fully nonlinear elliptic equations with Dirichlet boundary.
In this paper, we study the doubly reflected backward stochastic differential equations driven by G-Brownian motion. We show that the solution can be constructed by a family of penalized reflected G-BSDEs with a lower obstacle. The advantage of this
construction is that the convergence sequence is monotone, which is helpful to establish the relation between doubly reflected G-BSDEs and double obstacle fully nonlinear partial differential equations.
We study distribution dependent stochastic differential equations with irregular, possibly distributional drift, driven by an additive fractional Brownian motion of Hurst parameter $Hin (0,1)$. We establish strong well-posedness under a variety of as
sumptions on the drift; these include the choice $$B(cdot,mu) = fastmu(cdot) + g(cdot),quad f,gin B^alpha_{infty,infty}, quad alpha>1-1/2H,$$ thus extending the results by Catellier and Gubinelli [9] to the distribution dependent case. The proofs rely on some novel stability estimates for singular SDEs driven by fractional Brownian motion and the use of Wasserstein distances.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
