We construct an explicit one-to-one correspondence between non-relativistic stochastic processes and solutions of the Schrodinger equation relativistic Klein-Gordon equation. The existence this equivalence suggests that Lorentzian path integral can be defined as Ito integral, similar to definition Euclidean in terms Wiener integral. Moreover, result implies a interpretation quantum theories.

This paper presents a computational method for solving stochastic ItoVolterra integral equations. First, Haar wavelets and their properties are employed to derive a general procedure for forming the stochastic operational matrix of Haar wavelets. Then, application of this stochastic operational matrix for solving stochastic Ito-Volterra integral equations is explained. The convergence and error...

We develop a non-anticipative calculus for functionals of a continuous semimartingale, using an extension of the Ito formula to path-dependent functionals which possess certain directional derivatives. The construction is based on a pathwise derivative, introduced by B Dupire, for functionals on the space of right-continuous functions with left limits. We show that this functional derivative ad...

The present paper represents a continuation of paper [4], in which the existence and uniqueness problems for a general Ito–Volterra integrodifferential equation are investigated by using the concept of a non-linear random integral contractor. Since the Lipschitz condition and the random integral contractor for the coefficients of the considered equation, in general, cannot be compared, the noti...

Traditional control algorithms in Automatic Train Operation (ATO) system have some drawbacks, such as high energy consumption and low riding comfort. Combined with data mining methods and driving experience, two Intelligent Train Operation (ITO) models for the subway train control are proposed. Firstly the training data set was sorted out and sieved out from the real train operation data set by...

Random or stochastic integral equations are important in the study of many physical phenomena in life sciences, engineering, and technology 1–13 . Currently there are two basic versions of stochastic integral equations being studied bymathematical statisticians and probabilists namely, those integral equations involving Ito-Doob type of stochastic integrals and those which can be formed as prob...

   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...

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...