Stochastic Differential Equations Describing Systems with Coloured Noise

Author:

Kolářová Edita1,Brančík Lubomír2

Affiliation:

1. Department of Mathematics , Brno University of Technology , Brno , Czech Republic

2. Department of Radio Electronic , Brno University of Technology , Brno , Czech Republic

Abstract

Abstract In this paper we deal with stochastic differential equations, that describe systems effected by coloured noise. In electrical systems this can be the case, when e.g. transmission line is modelled by means of proper higher-order ladder network. We define the mathematical representation of the coloured noise as a solution of the Langevin equation and formulate the corresponding Itô type stochastic differential equation. Applying this theory we derive the stochastic model of the network and find sets of individual stochastic trajectories numerically via a stochastic version of the backward Euler scheme. Afterwards respective confi-dence intervals are computed statistically while utilizing Student’s t distribution. The theoretical results are illustrated by an example of a higher-order ladder network. Numerical simulations in the example are carried out using Matlab.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Reference10 articles.

1. [1] ARNOLD, L.: Stochastic Differential Equations: Theory and Applications. John Wiley & Sons, New York, 1974.

2. [2] ØKSENDAL, B.: Stochastic Differential Equations, An Introduction with Applications. Springer-Verlag, Berlin, 2000.

3. [3] BRANČÍK, L.: Time and Laplace-domain methods for MTL transient and sensitivity analysis, COMPEL—The International Journal for Computation and Mathematics in Electrical and Electronic Engineering 30, 2011, no. 4, 1205–1223.10.1108/03321641111133136

4. [4] KLOEDEN, P.—PLATEN, E.—SCHURZ, H.: Numerical Solution of SDE Through Computer Experiments. Springer-Verlag, Berlin, 1997.

5. [5] DZHALLADOVA, I.—MICHALKOVÁ, M.—RŮŽIČKOVÁ, M. : Model of stabilizing of the interest rate on deposits banking system using by moment equatioons Tatra Mt. Math. Publ. 54 (2013), 4–59.

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