We study Runge-Kutta methods for rough differential equations which can be used to calculate solutions stochastic driven by processes that are rougher than a Brownian motion. use Taylor series representation (B-series) both the numerical scheme and solution of equation in order determine conditions guarantee desired local error underlying method. Subsequently, we prove global given rate. In add...

This paper will introduce the Ito’s lemma used in stochastic calculus to obtain Ito-Taylor expansion of a differential equations. The Euler-Maruyama and Milstein’s methods solving equations be discussed derived. We apply these two numerical Black-Scholes model values European call option stock at discretized time intervals. use computer simulation approximate while using formula exact solution....

We discuss interplays between log-concave functions and log-concave sequences. We prove a Bernstein-type theorem, which characterizes the Laplace transform of logconcave measures on the half-line in terms of log-concavity of the alternating Taylor coefficients. We establish concavity inequalities for sequences inspired by the PrékopaLeindler and the Walkup theorems. One of our main tools is a s...

Using classical Taylor series techniques, we develop a unified approach to pricing and implied volatility for European-style options in a general local-stochastic volatility setting. Our price approximations require only a normal CDF and our implied volatility approximations are fully explicit (ie, they require no special functions, no infinite series and no numerical integration). As such, app...

chloride ion ingress in concrete is the main reason of concrete corrosion. in real world both uncertainty and stochasticity are main attributes of almost all measurements including testing and modeling of chloride content profile in concrete. regarding these facts new models should be able to represent at least some of the uncertainties in the predictions. in this paper after inspiration from c...

This paper concerns the Taylor-Aris dispersion of a dilute solute concentration immersed in a highly heterogeneous fluid flow having possibly sharp interfaces (discontinuities) in the diffusion coefficient and flow velocity. The focus is two-fold: (i) Calculation of the longitudinal effective dispersion coefficient, and (ii) sample path analysis of the underlying stochastic process governing th...

The current research attempts to offer a new method for solving fuzzy linear Volterra integral equations system. This method converts the given fuzzy system into a linear system in crisp case by using the Taylor expansion method. Now the solution of this system yields the unknown Taylor coefficients of the solution functions. The proposed method is illustrated by an example and also results are...

A class of discrete-time M=G=1 queues, including both round robin and last come rst served service, in which customers are subject to permutations is considered. These time slotted queues, analogous to the symmetric queues of Kelly, are analyzed by examination of the time reversed process. Product form stationary distributions are found for a type of doubly stochastic server of Schassberger [5]...