Application of Stochastic Differential Equations

Application of Stochastic Differential Equations

Paper in proceedings (conference paper)

Stochastic differential equations (the SDE) are used to describe physical phenomena. Solution of the stochastic model is a random process. Objective of the analysis of random processes is the construction of an appropriate model, which allows understanding the mechanisms. On their basis observed data are generated. Knowledge of the model also allows forecasting the future and it is possible to control and optimize the activity of the applicable system. In the presented contribution is to first defined probability space and Wiener process. On this basis it is defined the SDE and the basic properties are indicated. The final part contains examples illustrating the use of the SDE in practice.

Stochastic differential equations (the SDE) are used to describe physical phenomena. Solution of the stochastic model is a random process. Objective of the analysis of random processes is the construction of an appropriate model, which allows understanding the mechanisms. On their basis observed data are generated. Knowledge of the model also allows forecasting the future and it is possible to control and optimize the activity of the applicable system. In the presented contribution is to first defined probability space and Wiener process. On this basis it is defined the SDE and the basic properties are indicated. The final part contains examples illustrating the use of the SDE in practice.

random process, stochastic differential equations, Brownian motion, Wiener process, application

random process, stochastic differential equations, Brownian motion, Wiener process, application

KLIMEŠOVÁ, M.; BAŠTINEC, J.

20.06.2014

Vydavatelské oddělení UO

Brno

978-80-7231-961-9

Matematika, informatika a aplikované vědy

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