Local solution method for the problem of enlargement of filtration
The enlargement of filtration theory is a study of semimartingales when the basic filtration changes. This theory provides particular techniques on stochastic calculus. We present here a technique, that we call the local solution method. We will show, with several examples, that the local solution method is an effective and flexible method. In particular, with the local solution method, we will give a unified proof of three of the classical formulas, namely Jacod's formula, the progressive enlargement formula and the enlargement formula with honest time. We also show that, besides its generality, this method, necessiting long (but interesting) computations, may not be optimal.
In this paper, a numerical method is given for solving fuzzy Fredholm integral equations of the second kind, by using Bernstein piecewise polynomial, whose coefficients determined through solving dual fuzzy linear system. Numerical examples are presented to illustrate the proposed method, whose calculations were implemented by using the Computer software MathCadV.14.