Simulation of multiconductor transmission lines with random parameters via stochastic differential equations approach

Brančík, Lubomír; Kolarova, Edita

doi:10.1177/0037549716645198

Cited by 11 publications

(6 citation statements)

References 30 publications

(71 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The Γ r i r j symbol has been evaluated according to Eq. (35). We obtain the first order result in the variances 2 i of the stochastic variables µ i (t) from which we constructed the lognormal variables (Eq.…”

Section: Discussionmentioning

confidence: 99%

Extending the linear-noise approximation to biochemical systems influenced by intrinsic noise and slow lognormally distributed extrinsic noise

et al. 2019

View full text Add to dashboard Cite

It is well known that the kinetics of an intracellular biochemical network is stochastic. This is due to intrinsic noise arising from the random timing of biochemical reactions in the network as well as due to extrinsic noise stemming from the interaction of unknown molecular components with the network and from the cell's changing environment. While there are many methods to study the effect of intrinsic noise on the system dynamics, few exist to study the influence of both types of noise. Here we show how one can extend the conventional linear-noise approximation to allow for the rapid evaluation of the molecule numbers statistics of a biochemical network influenced by intrinsic noise and by slow lognormally distributed extrinsic noise. The theory is applied to simple models of gene regulatory networks and its validity confirmed by comparison with exact stochastic simulations. In particular we show how extrinsic noise modifies the dependence of the variance of the molecule number fluctuations on the rate constants, the mutual information between input and output signalling molecules and the robustness of feed-forward loop motifs.

show abstract

Section: Discussionmentioning

confidence: 99%

Extending the linear-noise approximation to biochemical systems influenced by intrinsic noise and slow lognormally distributed extrinsic noise

et al. 2019

View full text Add to dashboard Cite

show abstract

“…A generalization of multiconductor transmission line models can be found, e.g., in Brančík and Kolářová (2016). Besides the case of additive noises produced by external sources discussed in our paper, it is possible to consider multiplicative noises produced by a (Brančík and Kolářová, 2012, 2015.…”

Section: Discussionmentioning

confidence: 99%

“…Herein, we use an alternating-direction-implicit (ADI) iteration (Wachspress, 1988) to get the solution. It was verified that the procedure is stable and sufficiently fast for higher-order circuits too (Brančík and Kolářová, 2016). Then, designating V ¼ I ÀÃh; W ¼ ÀÃ T h and F nþ1 as the right-hand side of equation ( 24), we solve in each time step, n = 0, 1,. .…”

Section: Numerical Solutions 41 Direct Computation Of the Momentsmentioning

confidence: 99%

Confidence intervals for RLCG cell influenced by coloured noise

Kolarova

Brančík

2017

COMPEL

View full text Add to dashboard Cite

Purpose The purpose of this paper is to determine confidence intervals for the stochastic solutions in RLCG cells with a potential source influenced by coloured noise. Design/methodology/approach The deterministic model of the basic RLCG cell leads to an ordinary differential equation. In this paper, a stochastic model is formulated and the corresponding stochastic differential equation is analysed using the Itô stochastic calculus. Findings Equations for the first and the second moment of the stochastic solution of the coloured noise-affected RLCG cell are obtained, and the corresponding confidence intervals are determined. The moment equations lead to ordinary differential equations, which are solved numerically by an implicit Euler scheme, which turns out to be very effective. For comparison, the confidence intervals are computed statistically by an implementation of the Euler scheme using stochastic differential equations. Practical implications/implications The theoretical results are illustrated by examples. Numerical simulations in the examples are carried out using Matlab. A possible generalization for transmission line models is indicated. Originality/value The Itô-type stochastic differential equation describing the coloured noise RLCG cell is formulated, and equations for the respective moments are derived. Owing to this original approach, the confidence intervals can be found more effectively by solving a system of ordinary differential equations rather than by using statistical methods.

show abstract

“…Stochastic differential equations (SDEs) are used in numerous scientific disciplines, including epidemiology, mechanics, microelectronics and finance [1][2][3][4][5]. Numerical methods, which can be broadly categorized as explicit and implicit, are important tools for approximating solutions to these equations [1,6].…”

Section: Introductionmentioning

confidence: 99%

A split-step Euler-Maruyama based method with partial truncation coefficients for nonlinear SDEs

Haghighi

2024

Preprint

View full text Add to dashboard Cite

The main objective of this paper is to develop and analyze a numerical method for the strong approximation of solutions to highly nonlinear stiff It\^{o} stochastic differential equations (SDEs). In this method, we first divide the coefficients of the SDEs into linear and nonlinear parts. Then, in two fully explicit recursive phases, we apply the appropriate truncation transformation only to the nonlinear parts of the coefficients of the SDEs at each step. Theoretical aspects are introduced to establish the $L^q$-convergence theory of the new method in the finite time interval $[0,T]$. The stability and boundedness properties of the solutions generated by the new method are also investigated. An important contribution is that the region of MS-stability of the new method includes the region of MS-stability of the partially truncated method proposed by Yang et al. (2022). Moreover, we show that the proposed method preserves the exponential MS-stability and the asymptotic boundedness of the SDEs. Finally, numerical experiments are performed to compare the efficiency of this method with an existing explicit method developed for nonlinear SDEs. MSC Classification: 65C30 , 65L07 , 65L04

show abstract

Simulation of multiconductor transmission lines with random parameters via stochastic differential equations approach

Cited by 11 publications

References 30 publications

Extending the linear-noise approximation to biochemical systems influenced by intrinsic noise and slow lognormally distributed extrinsic noise

Extending the linear-noise approximation to biochemical systems influenced by intrinsic noise and slow lognormally distributed extrinsic noise

Confidence intervals for RLCG cell influenced by coloured noise

A split-step Euler-Maruyama based method with partial truncation coefficients for nonlinear SDEs

Contact Info

Product

Resources

About