TY - JOUR

T1 - Conditional Optimization of Algorithms for Estimating Distributions of Solutions to Stochastic Differential Equations

AU - Averina, Tatyana

PY - 2024/2

Y1 - 2024/2

N2 - This article discusses an alternative method for estimating marginal probability densities of the solution to stochastic differential equations (SDEs). Two algorithms for calculating the numerical–statistical projection estimate for distributions of solutions to SDEs using Legendre polynomials are proposed. The root-mean-square error of this estimate is studied as a function of the projection expansion length, while the step of a numerical method for solving SDE and the sample size for expansion coefficients are fixed. The proposed technique is successfully verified on three one-dimensional SDEs that have stationary solutions with given one-dimensional distributions and exponential correlation functions. A comparative analysis of the proposed method for calculating the numerical–statistical projection estimate and the method for constructing the histogram is carried out.

AB - This article discusses an alternative method for estimating marginal probability densities of the solution to stochastic differential equations (SDEs). Two algorithms for calculating the numerical–statistical projection estimate for distributions of solutions to SDEs using Legendre polynomials are proposed. The root-mean-square error of this estimate is studied as a function of the projection expansion length, while the step of a numerical method for solving SDE and the sample size for expansion coefficients are fixed. The proposed technique is successfully verified on three one-dimensional SDEs that have stationary solutions with given one-dimensional distributions and exponential correlation functions. A comparative analysis of the proposed method for calculating the numerical–statistical projection estimate and the method for constructing the histogram is carried out.

KW - Legendre polynomials

KW - histogram

KW - marginal probability density

KW - numerical–projection estimate

KW - stochastic differential equations

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85187267712&origin=inward&txGid=42a7af55e7d25a9b404a655621e48a8f

UR - https://www.mendeley.com/catalogue/70eef43f-7c2a-3899-92ef-ea5453c096ee/

U2 - 10.3390/math12040586

DO - 10.3390/math12040586

M3 - Article

VL - 12

JO - Mathematics

JF - Mathematics

SN - 2227-7390

IS - 4

M1 - 586

ER -