DEVELOPMENT OF MOMENT-SEMIINVARIANT SOFTWARE FOR STOCHASTIC ANALYSIS

Abstract

The article describes the methodological foundations and the results of comparative testing of scientific software for stochastic analysis of multidimensional nonlinear stochastic systems (StS) described by stochastic differential equations, developed on the basis of the modified moment-semi-invariant method (M2SM) and orthogonal factorization of the unknown one-dimensional density of the system state vector by the bi-orthogonal system of polynomials. We have obtained exact differential equations for the components of the expectation vector, the covariance matrix, and the higher initial moments of the state vector of the nonlinear StS, described by the Ito stochastic differential equation containing non-polynomial coefficients (continuous or having first-kind discontinuous points) and a vector random process with independent increments. Software “StS-Analysis-M2SM” contains the modules developed by the author, which allow you to partially automate actions to compile a closed-loop system of differential equations for parameters of the state vector of a nonlinear StS. Software “StS-Analysis-M2SM” is developed in the Python language and is compatible with new domestic processors and high-performance platforms. Verification of the performance of the software “StS-Analysis-M2SM“ was carried out using examples of non-linear StS that have exact solutions. The results were compared with the normal approximation method (NAM) and the ellipsoidal approximation method (EAM). M2SM gives a high accuracy (less than 2%) of determining the expectation function and the covariance matrix of the state vector of the StS, complying with the system of ordinary differential equations for the expectation function components, the covariance matrix and probabilistic higher initial moments included in the right-hand parts of the exact open equations for the expectation and covariance matrix. Software “StS-Analysis-M2SM” can be applied in scientific research; for training in higher education in the courses “Random Processes”, “Theory of Stochastic Differential Systems”, etc.; in the management of technical, organizational and economical, environmental and other systems.

Keywords

• Stochastic process
• stochastic analysis
• stochastic system
• stochastic differential equation
• mathematical expectation
• covariance matrix
• probability moment
• modified moment-semiinvariant method (М2 SIM)