ترغب بنشر مسار تعليمي؟ اضغط هنا

Forward-backward SDEs with distributional coefficients

147   0   0.0 ( 0 )
 نشر من قبل Elena Issoglio
 تاريخ النشر 2016
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

Forward-backward stochastic differential equations (FBSDEs) have attracted significant attention since they were introduced almost 30 years ago, due to their wide range of applications, from solving non-linear PDEs to pricing American-type options. Here, we consider two new classes of multidimensional FBSDEs with distributional coefficients (elements of a Sobolev space with negative order). We introduce a suitable notion of a solution, show existence and uniqueness of a strong solution of the first FBSDE, and weak existence for the second. We establish a link with PDE theory via a nonlinear Feynman-Kac representation formula. The associated semi-linear second order parabolic PDE is the same for both FBSDEs, also involves distributional coefficients and has not previously been investigated; our analysis uses mild solutions, Sobolev spaces and semigroup theory.



قيم البحث

اقرأ أيضاً

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.
99 - Guohuan Zhao 2020
We prove the existence and uniqueness for SDEs with random and irregular coefficients through solving a backward stochastic Kolmogorov equation and using a modified Zvonkins type transformation.
In this work, we study the numerical approximation of a class of singular fully coupled forward backward stochastic differential equations. These equations have a degenerate forward component and non-smooth terminal condition. They are used, for exam ple, in the modeling of carbon market[9] and are linked to scalar conservation law perturbed by a diffusion. Classical FBSDEs methods fail to capture the correct entropy solution to the associated quasi-linear PDE. We introduce a splitting approach that circumvent this difficulty by treating differently the numerical approximation of the diffusion part and the non-linear transport part. Under the structural condition guaranteeing the well-posedness of the singular FBSDEs [8], we show that the splitting method is convergent with a rate $1/2$. We implement the splitting scheme combining non-linear regression based on deep neural networks and conservative finite difference schemes. The numerical tests show very good results in possibly high dimensional framework.
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.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا