In this paper we provide existence and uniqueness results for the solution of BSDEs driven by a general square-integrable martingale under partial information. We discuss some special cases where the solution to a BSDE under restricted information can be derived by that related to a problem of a...

The motivation of this paper is to prove verification theorems for stochastic optimal control of finite dimensional diffusion processes without control in the diffusion term, in the case where the value function is assumed to be continuous in time and once differentiable in the space variable...

This paper is devoted to presenting a method of proving verification theorems for stochastic optimal control of finite dimensional diffusion processes without control in the diffusion term. The value function is assumed to be continuous in time and once differentiable in the space variable...

If X and Y are two general stochastic processess, we define a covariation process [X, Y] with the help of a limit procedure. When the processes are semimartingales, [X, Y] is their classical bracket. We calculate covariation for some important examples arising from anticipating stochastic...

Let M be a normal martingale (i.e. <M, M> (t) = t), we decompose the product of two multiple stochastic integrals (with respect to M) In(f)Im(g) as a sum of n [logical and] m terms Hk. Hk is equal to the integral over k+ of the function t -- In+m-2k(hk(t,.)), with respect to the k-tensor product of...</m,>

In this paper, we introduce first a natural generalization of the concept of Dirichlet process, providing significant examples. The second important tool concept is the n-covariation and the related n-variation. The n-variation of a continuous process and the n-covariation of a vector of...

This paper is devoted to analyzing several properties of the bifractional Brownian motion introduced by Houdré and Villa. This process is a self-similar Gaussian process depending on two parameters H and K and it constitutes a natural generalization of fractional Brownian motion (which is...