اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدp-integrable solutions to multidimensional BSDEs and degenerate systems of PDEs with logarithmic nonlinearities
140
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We study multidimensional backward stochastic differential equations (BSDEs) which cover the logarithmic nonlinearity u log u. More precisely, we establish the existence and uniqueness as well as the stability of p-integrable solutions (p > 1) to multidimensional BSDEs with a p-integrable terminal condition and a super-linear growth generator in the both variables y and z. This is done with a generator f(y, z) which can be neither locally monotone in the variable y nor locally Lipschitz in the variable z. Moreover, it is not uniformly continuous. As application, we establish the existence and uniqueness of Sobolev solutions to possibly degenerate systems of semilinear parabolic PDEs with super-linear growth generator and an p-integrable terminal data. Our result cover, for instance, certain (systems of) PDEs arising in physics.
قيم البحث
اقرأ أيضاً
In this paper, we are interested in solving general time interval multidimensional backward stochastic differential equations in $L^p$ $(pgeq 1)$. We first study the existence and uniqueness for $L^p$ $(p>1)$ solutions by the method of convolution an
d weak convergence when the generator is monotonic in $y$ and Lipschitz continuous in $z$ both non-uniformly with respect to $t$. Then we obtain the existence and uniqueness for $L^1$ solutions with an additional assumption that the generator has a sublinear growth in $z$ non-uniformly with respect to $t$.
This paper is devoted to solving a multidimensional backward stochastic differential equation with a general time interval, where the generator is uniformly continuous in $(y,z)$ non-uniformly with respect to $t$. By establishing some results on dete
rministic backward differential equations with general time intervals, and by virtue of Girsanovs theorem and convolution technique, we establish a new existence and uniqueness result for solutions of this kind of backward stochastic differential equations, which extends the results of Hamadene (2003) and Fan, Jiang, Tian (2011) to the general time interval case.
We are interested in path-dependent semilinear PDEs, where the derivatives are of G{^a}teaux type in specific directions k and b, being the kernel functions of a Volterra Gaussian process X. Under some conditions on k, b and the coefficients of the P
DE, we prove existence and uniqueness of a decoupled mild solution, a notion introduced in a previous paper by the authors. We also show that the solution of the PDE can be represented through BSDEs where the forward (underlying) process is X.
Motivated by an equilibrium problem, we establish the existence of a solution for a family of Markovian backward stochastic differential equations with quadratic nonlinearity and discontinuity in $Z$. Using unique continuation and backward uniqueness
, we show that the set of discontinuity has measure zero. In a continuous-time stochastic model of an endowment economy, we prove the existence of an incomplete Radner equilibrium with nondegenerate endogenous volatility.
In [4], the existence of the solution is proved for a scalar linearly growing backward stochastic differential equation (BSDE) if the terminal value is $Lexp{left(mu sqrt{2log{(1+L)}},right)}$-integrable with the positive parameter $mu$ being bigger
than a critical value $mu_0$. In this note, we give the uniqueness result for the preceding BSDE.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
