We study an inverse problem for the fractional Schr\"odinger equation (FSE) with a local perturbation by linear partial differential operator (PDO) of order smaller than Laplacian. show that one can uniquely recover coefficients PDO from Dirichlet-to-Neumann (DN) map associated to perturbed FSE. This is proved two classes coefficients: which belong certain spaces Sobolev multipliers and bounded...

A control problem for a linear stochastic system with an arbitrary fractional Brownian motion and a cost functional that is quadratic in the system state and the control is solved. An optimal control is given explicitly as the sum of a prediction of the future fractional Brownian motion and the well known linear feedback control for the associated deterministic linear-quadratic control problem....

We compute all signatures of PSL2(

Using the multiple stochastic integrals we prove an existence and uniqueness result for a linear stochastic equation driven by the fractional Brownian motion with any Hurst parameter. We study both the one parameter and two parameter cases. When the drift is zero, we show that in the one-parameter case the solution in an exponential, thus positive, function while in the two-parameter settings t...