We formulate a notion of doubly reflected BSDE in the case where the barriers xi and zeta do not satisfy any regularity assumption. Under a technical assumption (a Mokobodzki-type condition), we show existence and uniqueness of the solution. In the case where xi is right upper-semicontinuous and...

We formulate a notion of doubly reflected BSDE in the case where the barriers xi and zeta do not satisfy any regularity assumption. Under a technical assumption (a Mokobodzki-type condition), we show existence and uniqueness of the solution. In the case where xi is right upper-semicontinuous and...

We consider the optimal stopping problem with non-linear f-expectation (induced by a BSDE) without making any regularity assumptions on the reward process xi. We show that the value family can be aggregated by an optional process Y . We characterize the process Y as the Ef-Snell envelope of xi....

We consider the optimal stopping problem with non-linear f-expectation (induced by a BSDE) without making any regularity assumptions on the reward process xi. We show that the value family can be aggregated by an optional process Y . We characterize the process Y as the Ef-Snell envelope of xi....

In the first part of the paper, we study reflected backward stochastic differential equations (RBSDEs) with lower obstacle which is assumed to be right upper-semicontinuous but not necessarily right-continuous. We prove existence and uniqueness of the solutions to such RBSDEs in appropriate...

Given a fractional Brownian motion , with Hurst parameter , we study the properties of all solutions of A different stochastic calculus is required for the process because it is not a semimartingale.

We consider the problem of efficient estimation for the drift of fractional Brownian motion with hurst parameter H less than . We also construct superefficient James-Stein type estimators which dominate, under the usual quadratic risk, the natural maximum likelihood estimator.

In this paper, we study necessary and sufficient conditions for the equivalence of Volterra Gaussian processes.

In this paper, we construct a noncanonical representation with respect to the Brownian motion B of the form which has an infinite-dimensional orthogonal complement. Moreover we study some properties of the kernel [rho] and we discuss the -semimartingale property.

We give a link between stochastic processes which are infinitely divisible with respect to time (IDT) and Lévy processes. We investigate the connection between the selfsimilarity and the strict stability for IDT processes. We also consider a subordination of a Lévy process by an increasing IDT...