Di Paola and Falsone’s formula is widely used in expressing a correction term to the usual Ito integral in stochastic dynamical systems with parametric Poisson white noise. An alternative expression is presented here. Comparing with Di Paola and Falsone’s original expression, the alternative one is applicable under more general conditions, and shows significantly improved performance in numeric...

in this paper, indium tin oxide (ito) nanoparticles has been prepared by chemical methods under given conditions with solution of indium chloride (incl3·4h2o), tin chloride (sncl4·5h2o) in ammonia solution. the samples were characterized by x-ray diffraction (xrd) and scanning electron microscopy (sem) analyses after heat treatments. the sem results showed that, the size of the ito particles pr...

where (x(£),x(0) = 0,0fktfíl\ is a Brownian motion process. Equation (0.1) has been studied by S. Bernstein [l], J. L. Doob [5] and others [2], [ 10]. In general, the solution given here is different from that given by these authors. Equation (0.1) is almost purely formal since the derivative dx/dt fails to exist with probability one. In [2], [5], [ 10], the stochastic integral of K. Ito [7], [...

Herein, a stepwise electrodeposition technique was used to synthesize the Pd based nanoparticles on indium-tin oxide (ITO) electrodes. First of all, Pd nanoparticles were electrodeposited on ITO via one step electrodeposition technique. Furthermore, Au was electrodeposited on Pd. Finally, Co was electrodeposited on Au and Pd electrodeposited ITO electrode via stepwise electrodeposition techniqu...

In this paper we look at several (trigonometric) stochastic differential equations, find the general form for such nonlinear equation by using I'to formula. Then exact solution different trigonometric equations use of integrals. Ilustrate approach with various examples. (Precise Ito integral formula) and approximate (numerical approximation (the Euler-Maruyama technique Milstein method) were co...

Stochastic or random integral equations are extremely important in the study of many physical phenomena in life sciences and engineering [3, 14, 16]. There are currently two basic versions of stochastic integral equations being studied by probabilists and mathematical statisticians, namely, those integral equations involving Ito-Doob type of stochastic integrals and those which can be formed as...