Open AccessConstruction of stochastic transport models with a constant function
Author(s) -
Elena Karachanskaya,
Tatiana Tagirova
Publication year - 2019
Publication title -
iop conference series. earth and environmental science
Language(s) - English
Resource type - Journals
eISSN - 1755-1307
pISSN - 1755-1315
DOI - 10.1088/1755-1315/403/1/012211
Subject(s) - stochastic differential equation , constant (computer programming) , stochastic modelling , stochastic partial differential equation , mathematics , component (thermodynamics) , constant coefficients , continuous time stochastic process , function (biology) , stochastic process , differential equation , mathematical optimization , computer science , mathematical analysis , physics , statistics , evolutionary biology , biology , thermodynamics , programming language
The paper considers two transport models described using stochastic differential equations system. The investigation is based on a constant function of motion. The approach allows building stochastic dynamical model using a well-known deterministic model and its constant function. The construction algorithm is realized as a software, and it allows choosing a set of functions for simulation. Moreover, it is possible to construct both a system of stochastc differential equations and a system of deterministic ones. The article represents a stochastic model for a vehicle movement and an idea for an itinerant aircraft stochastic model. Transit from a deterministic model to stochastic one is carried out by completing of three addition terms. The first term is a continuous random influence. The second one describes strong random jumps. The third item is an addition component for a drift coefficient. It was shown that choice of additional functions allows building a system of equations with such coefficients that the resolution of this system meets reasonable restrictions. Examples of numerical solutions of the equations constructed confirm the conservation of the value of dynamic invariant under any solution of stochastic differential equations system.