arXiv subjects

Bujar Gashi

Publications and source records attributed to Bujar Gashi.

4 recordsLinked to original sources

arXiv2018

Backward stochastic differential equations with unbounded generators

In this paper we consider two classes of backward stochastic differential equations. Firstly, under a Lipschitz-type condition on the generator of the equation, which can also be unbounded, we give sufficient conditions for the existence of a unique solution pair. The method of proof is that of Picard iterations and the resulting conditions are new. We also prove a comparison theorem. Secondly, under the linear growth and continuity assumptions on the possibly unbounded generator, we prove the existence of the solution pair. This class of equations is more general than the existing ones.

math.PR↗

arXiv2016

Voronoi means, moving averages, and power series

We introduce a {\it non-regular} generalisation of the Nörlund mean, and show its equivalence with a certain moving average. The Abelian and Tauberian theorems establish relations with convergent sequences and certain power series. A strong law of large numbers is also proved.

math.CA↗

arXiv2014

Stochastic minimum-energy control

We give the solution to the minimum-energy control problem for linear stochastic systems. The problem is as follows: given an exactly controllable system, find the control process with the minimum expected energy that transfers the system from a given initial state to a desired final state. The solution is found in terms of a certain forward-backward stochastic differential equation of Hamiltonian type.

math.PR↗

arXiv2014

Logarithmic moving averages

We introduce a moving average summability method, which is proved to be equivalent with the logarithmic $\ell$-method. Several equivalence and Tauberian theorems are given. A strong law of large numbers is also proved.

math.CA↗