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...

   High transparent conductive indium tin oxide/titanium dioxide (ITO/TiO2) nanostructured thin film is prepared by sol-gel dip-coating technique. This method yielded monodisperse ITO nanoparticles with mean diameter of 12 nm. The atomic composition of the Sn within the ITO structure changed from 0-20 wt.%. Through controlled annealing temperature at 550 oC, the result...

We prove optimality principles for continuous bounded nonnegative viscosity solutions of Hamilton-Jacobi-Bellman equations. In particular we provide a representation formula for viscosity supersolutions as value functions of suitable obstacle control problems. This representation formula is applied to extend the Lyapunov direct method for stability to controlled Ito stochastic differential equa...

indium tin oxide (ito) thin films were deposited on glass substrates by rf sputtering using an ito ceramic target (in2o3-sno2, 90-10 wt. %). after deposition, samples were annealed at different temperatures in vacuum furnace. the post vacuum annealing effects on the structural, optical and electrical properties of ito films were investigated. polycrystalline ito films have been analyzed in wide...

This paper investigates the pricing formula for barrier options where underlying asset is driven by sub-mixed fractional Brownian motion with jump. By applying corresponding Ito^’s formula, B-S type PDE derived a self-financing strategy. Furthermore, explicit obtained through converting to Cauchy problem. Numerical experiments are conducted test impact of price, Hurst index, jump intensity and ...

Stochastic differential equations and the Black-Scholes PDE. We derived the BlackScholes formula by using arbitrage (risk-neutral) valuation in a discrete-time, binomial tree setting, then passing to a continuum limit. This section explores an alternative, continuoustime approach via the Ito calculus and the Black-Scholes differential equation. This material is very standard; I like Wilmott-How...

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...

This paper considers the problem of partial finite-time synchronization between switched stochastic Chua’s circuits accompanied by a time-driven switching law. Based on the Ito formula and Lyapunov stability theory, a sliding-mode controller is developed to guarantee the synchronization of switched stochastic master-slave Chua’s circuits and for the mean of error states to obtain the partial fi...