اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدMulti-dimensional BSDEs driven by $G$-Brownian motion and related system of fully nonlinear PDEs
84
0
0.0
(
0
)
تأليف
Guomin Liu
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In this paper, we study the well-posedness of multi-dimensional backward stochastic differential equations driven by $G$-Brownian motion ($G$-BSDEs) with diagonal generators, the $z$ parts of whose $l$-th components only depend on the $l$-th columns. The existence and uniqueness of solutions are obtained via a contraction argument for $Y$ component and a backward iteration of local solutions. Furthermore, we show that, the solution of multi-dimensional $G$-BSDE in a Markovian framework provides a probabilistic formula for the viscosity solution of a system of nonlinear parabolic partial differential equations.
قيم البحث
اقرأ أيضاً
We consider the well-posedness problem of multi-dimensional reflected backward stochastic differential equations driven by $G$-Brownian motion ($G$-BSDEs) with diagonal generators. Two methods, i.e., the penalization method and the Picard iteration a
rgument, are provided to prove the existence and uniqueness of solutions. We also study its connection with the obstacle problem of a system of fully nonlinear PDEs.
In this paper, we study the reflected solutions of one-dimensional backward stochastic differential equations driven by G-Brownian motion (RGBSDE for short). The reflection keeps the solution above a given stochastic process. In order to derive the u
niqueness of reflected GBSDEs, we apply a martingale condition instead of the Skorohod condition. Similar to the classical case, we prove the existence by approximation via penalization.
In this paper, we consider a reflected backward stochastic differential equation driven by a $G$-Brownian motion ($G$-BSDE), with the generator growing quadratically in the second unknown. We obtain the existence by the penalty method, and a priori e
stimates which implies the uniqueness, for solutions of the $G$-BSDE. Moreover, focusing our discussion at the Markovian setting, we give a nonlinear Feynman-Kac formula for solutions of a fully nonlinear partial differential equation.
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.
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.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
