We present a systematic method for computing explicit approximations to martingale representations for a large class of Brownian functionals. The approximations are based on a notion of pathwise functional derivative and yield a consistent estimator for the integrand in the martingale representation formula for any square-integrable functional of the solution of an SDE with path-dependent coeff...

Many time-varying phenomena of various fields in science and engineering can be modeled as a stochastic differential equations, so investigation of conditions for existence of solution and obtain the analytical and numerical solutions of them are important. In this paper, the Adomian decomposition method for solution of the stochastic differential equations are improved.  Uniqueness and converg...

In this paper, the Kalman-Bucy filter is designed for an Ito-Volterra process over Ito-Volterra observations that cannot be reduced to the case of a differential observation equation. The Kalman-Bucy filter is then designed for an Ito-Volterra process over discontinuous Ito-Volterra observations. Based on the obtained results, the filtering problem over discrete observations with delays is solv...

in this article,we present a wavelet method for solving stochastic volterra integral equations based on haar wavelets. first, we approximate all functions involved in the problem by haar wavelets then, by substituting the obtained approximations in the problem, using the it^{o} integral formula and collocation points then, the main problem changes into a system of linear or nonlinear equation w...

Since the fractional Brownian motion is not a semi–martingale, the usual Ito calculus cannot be used to define a full stochastic calculus. However, in this work, we obtain the Itô formula, the Itô–Clark representation formula and the Girsanov theorem for the functionals of a fractional Brownian motion using the stochastic calculus of variations.

Since the fractional Brownian motion is not a semiimartingale, the usual Ito calculus cannot be used to deene a full stochastic calculus. However, in this work, we obtain the Itt formula, the ItttClark representation formula and the Girsanov theorem for the functionals of a fractional Brownian motion using the stochastic calculus of variations.

We introduce the stochastic integration with respect to the infinite-dimensional fractional Brownian motion. Using the techniques of the anticipating stochastic calculus, we derive an Itô formula for Hurst parameter bigger than 1 2 .

An Itô-type formula is given for an asymptotically 4-stable process.