Bernstein Polynomials and Brownian Motion

Approximation of Second-Order Moment Processes from Local Averages

In the literature, very few researchers considered approximating Brownian motion using Bernstein polynomials. Kowalski 1 is the first one who uses this method. In fact, if we restrict Brownian motion on 0, 1 , it is a real process with finite second order moment. In this paper, we will approximate all of the complex second order moment processes on a, b by Bernstein polynomials and other classi...

On the average number of sharp crossings of certain Gaussian random polynomials

Numerical solution of delay differential equations via operational matrices of hybrid of block-pulse functions and Bernstein polynomials

In this paper, we introduce hybrid of block-pulse functions and Bernstein polynomials and derive operational matrices of integration, dual, differentiation, product and delay of these hybrid functions by a general procedure that can be used for other polynomials or orthogonal functions. Then, we utilize them to solve delay differential equations and time-delay system. The method is based upon e...

The Numerical Solution of Some Optimal Control Systems with Constant and Pantograph Delays via Bernstein Polynomials

‎In this paper‎, ‎we present a numerical method based on Bernstein polynomials to solve optimal control systems with constant and pantograph delays‎. ‎Constant or pantograph delays may appear in state-control or both‎. ‎We derive delay operational matrix and pantograph operational matrix for Bernstein polynomials then‎, ‎these are utilized to reduce the solution of optimal control with constant...

A numerical study of electrohydrodynamic flow analysis in a circular cylindrical conduit using orthonormal Bernstein polynomials

In this work, the nonlinear boundary value problem in electrohydrodynamics flow of a fluid in an ion-drag configuration in a circular cylindrical conduit is studied numerically. An effective collocation method, which is based on orthonormal Bernstein polynomials is employed to simulate the solution of this model. Some properties of orthonormal Bernstein polynomials are introduced and utilized t...