Weak Backward Error Analysis for SDEs
نویسندگان
چکیده
منابع مشابه
Weak Backward Error Analysis for SDEs
We consider numerical approximations of stochastic differential equations by the Euler method. In the case where the SDE is elliptic or hypoelliptic, we show a weak backward error analysis result in the sense that the generator associated with the numerical solution coincides with the solution of a modified Kolmogorov equation up to high order terms with respect to the stepsize. This implies th...
متن کاملOn weak solutions of forward–backward SDEs
In this paper we continue exploring the notion of weak solution of forward–backward stochastic differential equations (FBSDEs) and associated forward–backward martingale problems (FBMPs). The main purpose of this work is to remove the constraints on the martingale integrands in the uniqueness proofs in our previous work (Ma et al. in Ann Probab 36(6):2092–2125, 2008). We consider a general clas...
متن کاملWeak Solutions for Forward – Backward Sdes — a Martingale Problem Approach
In this paper, we propose a new notion of Forward–Backward Martingale Problem (FBMP), and study its relationship with the weak solution to the forward–backward stochastic differential equations (FBSDEs). The FBMP extends the idea of the well-known (forward) martingale problem of Stroock and Varadhan, but it is structured specifically to fit the nature of an FBSDE. We first prove a general suffi...
متن کاملWeak Solutions of Forward-Backward SDEs and Their Uniqueness
In this paper we propose a new notion of Forward-Backward Martingale Problem (FBMP), and study its relationship with the weak solution to the backward stochastic differential equations. The FBMP extends the idea of the well-known (forward) martingale problem of Stroock and Varadhan, but it is structured specifically to fit the nature of a forward-backward stochastic differential equation (FBSDE...
متن کاملWeak error for stable driven SDEs : expansion of the densities
Consider a multidimensional SDE of the form Xt = x + ∫ t 0 b(Xs−)ds + ∫ t 0 f(Xs−)dZs where (Zs)s≥0 is a symmetric stable process. Under suitable assumptions on the coefficients the unique strong solution of the above equation admits a density w.r.t. the Lebesgue measure and so does its Euler scheme. Using a parametrix approach, we derive an error expansion w.r.t. the time step for the differen...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Numerical Analysis
سال: 2012
ISSN: 0036-1429,1095-7170
DOI: 10.1137/110831544