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

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  • Tatyana Averina

    (Institute of Computational Mathematics and Mathematical Geophysics, The Siberian Branch, The Russian Academy of Sciences, Novosibirsk State University, 630090 Novosibirsk, Russia)

Abstract

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.

Suggested Citation

  • Tatyana Averina, 2024. "Conditional Optimization of Algorithms for Estimating Distributions of Solutions to Stochastic Differential Equations," Mathematics, MDPI, vol. 12(4), pages 1-16, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:4:p:586-:d:1339884
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    References listed on IDEAS

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    1. Andrey Borisov, 2024. "Regime Tracking in Markets with Markov Switching," Mathematics, MDPI, vol. 12(3), pages 1-27, January.
    2. Konstantin Rybakov, 2023. "Spectral Representations of Iterated Stochastic Integrals and Their Application for Modeling Nonlinear Stochastic Dynamics," Mathematics, MDPI, vol. 11(19), pages 1-23, September.
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