We consider the problem of the construction of the asymptotically distribution free test by the observations of ergodic diffusion process. It is supposed that under the basic hypothesis the trend coefficient depends on a finite-dimensional parameter and we study the Cramér-von Mises type...

In this paper, we are concerned with backward stochastic differential equations (BSDE for short) of the following type: where q is a positive constant and [xi] is a random variable such that . We study the link between these BSDE and the associated Cauchy problem with terminal data g, where...

We study the existence of a minimal supersolution for backward stochastic differential equations when the terminal data can take the value +$\infty$ with positive probability. We deal with equations on a general filtered probability space and with generators satisfying a general monotonicity...