Stability in D of martingales and backward equations under discretization of filtration

Numerical algorithms for backward stochastic differential equations with 1-d brownian motion: Convergence and simulations

“…We should point out that there have been many recent different algorithms for computing solutions of BSDEs and the related results in numerical analysis, for example [1][2][3][4][5][6][7][8]10,11,14,16,17,[23][24][25]. In contrast to these results, our method uses very simple method.…”

Some examples and counterexamples of convergence of σ-algebras and filtrations

“…It happens that we have been interested, for the first time, in the convergence of filtrations observing discretizations of processes in relation to the behavior of filtrations generated by these discretizations when the mesh of discrefization tends to 0 (see [2]). We state here the following question.…”

“…How can one approximate 5r-martingales by martingales adapted to the filtrations generated by Y"? This question was studied in several directions in [2] with an application in the framework of backward stochastic differential equations; the connection with the convergence of filtrations was established in [3], where the relations between the convergence of processes and the convergence of the corresponding generated filtrations were studied in detail. In this paper, we are interested in the weak convergence of sequences of a-algebras and filtrations themselves.…”

Discretization of backward semilinear stochastic evolution equations

“…F is its natural filtration. Random walk W n and its filtration are defined by (6) and (7). W n are stochastic processes with independent increment.…”

“…Chevance also gave a space discretization to obtain a numerical scheme for solving the problem of BSDE. Independent of the work [3], Coquet, Mackevicius and Mémin [7,8] proved the convergence using the tool of convergence of filtrations. Briand, Delyon and Mémin [9,10] got the general convergence result with the above tool.…”