One of the main tasks to analyze and design a mining system is predicting the behavior exhibited by prices in the future. In this paper, the applications of different prediction methods are evaluated in econometrics and financial management fields, such as ARIMA, TGARCH, and stochastic differential equations, for the time-series of monthly copper prices. Moreover, the performance of these metho...

A new algorithm of determination of coe cients of multidimensional heat equations on the basis of temperature measurements is proposed. A system of stochastic di erential equations (SDE) can be assigned to a linear multidimensional heat equation. The solution of the heat equation can be obtained by solving the corresponding SDE by the method of statistical modeling. The sensitivity analysis is ...

We develop a weak exact simulation technique for a process X defined by a multidimensional stochastic differential equation (SDE). Namely, for a Lipschitz function g, we propose a simulation based approximation of the expectation E[g(Xt1 , · · · , Xtn)], which by-passes the discretization error. The main idea is to start instead from a wellchosen simulatable SDE whose coefficients are up-dated ...

In this article, we introduce a backward method to model stochastic gene expression and protein-level dynamics. The protein amount is regarded as a diffusion process and is described by a backward stochastic differential equation (BSDE). Unlike many other SDE techniques proposed in the literature, the BSDE method is backward in time; that is, instead of initial conditions it requires the specif...

We design numerical schemes for a class of slow-fast systems stochastic differential equations, where the fast component is an Ornstein-Uhlenbeck process and slow driven by fractional Brownian motion with Hurst index H>1/2. establish asymptotic preserving property proposed scheme: when time-scale parameter goes to 0, limiting scheme which consistent averaged equation obtained. With this analysi...

This paper studies an insurer's optimal investment portfolio under the mean-variance criterion. The financial market consists of a riskless bond and risky asset, latter's volatility is random. We are extending Cox–Ingersoll–Ross (CIR) model to case with jumps, where it modeled by jump-diffusion stochastic differential equation (SDE). use Lévy SDE describe risk process we have, in which extend c...

Stochastic differential equations (SDEs) provide accessible mathematical models that combine deterministic and probabilistic components of dynamic behavior. This article is an overview of numerical solution methods for SDEs. The solutions are stochastic processes that represent diffusive dynamics, a common modeling assumption in many application areas. We include a description of fundamental nu...

Biological processes measured repeatedly among a series of individuals are standardly analyzed by mixed models. Recently, stochastic processes have been introduced to model the variability along time for each subject. Although the likelihood of these stochastic mixed models is intractable, various estimation methods have been proposed when the latent stochastic process is a discrete time finite...

MOTIVATION The explosion of microarray studies has promised to shed light on the temporal expression patterns of thousands of genes simultaneously. However, available methods are far from adequate in efficiently extracting useful information to aid in a greater understanding of transcriptional regulatory network. Biological systems have been modeled as dynamic systems for a long history, such a...

This work concerns continuous-time, continuous-space stochastic dynamical systems described by differential equations (SDE). It presents a new approach to compute probabilistic safety regions, namely sets of initial conditions the SDE associated trajectories that are safe with probability larger than given threshold. The introduces functional is minimised at border region, then solves an optimi...