scientific article; zbMATH DE number 6992775

zbMath1404.60002MaRDI QIDQ4561589

D. F. Kuznetsov

Publication date: 12 December 2018

Full work available at URL: http://diffjournal.spbu.ru/pdf/kuznetsovdf2018.pdf

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zbMATH Keywords

stochastic differential equationnumerical methodstrong convergenceweak convergencenumerical integrationstochastic Taylor expansionweak approximationmultiple Fourier seriesLegendre polynomialnumerical modelingstrong approximationmean-square convergenceimplicit numerical methodParseval equalitymultiple trigonometric Fourier seriesStratonovich stochastic integralItō stochastic differential equationfinite-difference numerical methodMATLAB programexplicit numerical methodTaylor-Stratonovich expansionItō stochastic integralmultiple Fourier-legemdre seriesmultiple Itō stochastic integralmultiple stochastic integral expansionmultiple Stratonovich stochastic integralnumerical method of Runge-Kutta typeone-step numerical methodstochastic differential equation with jump componentstochastic integral on martingalestochastic integral on Poisson measurestrong numerical methodTaylor-Itō expansionthree-step numerical methodtwo-step numerical methodunified Taylor-Itō expansionunified Taylor-Stratonovich expansionweak numerical method

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Research exposition (monographs, survey articles) pertaining to numerical analysis (65-02) Stochastic integrals (60H05) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) Research exposition (monographs, survey articles) pertaining to probability theory (60-02)

Related Items (14)

The Proof of Convergence with Probability 1 in the Method of Expansion of Iterated Ito Stochastic Integrals Based on Generalized Multiple Fourier Series ⋮ Application of Multiple Fourier-Legendre Series to Implementation of Strong Exponential Milstein and Wagner-Platen Methods for Non-Commutative Semilinear Stochastic Partial Differential Equations ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Explicit one-step numerical method with the strong convergence order of 2.5 for Ito stochastic differential equations with a multi-dimensional nonadditive noise based on the Taylor-Stratonovich expansion ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Modeling and analysis of output processes of linear continuous stochastic systems based on orthogonal expansions of random functions ⋮ Application of the Method of Approximation of Iterated Ito Stochastic Integrals Based on Generalized Multiple Fourier Series to the High-Order Strong Numerical Methods for Non-Commutative Semilinear Stochastic Partial Differential Equations

Uses Software

• Matlab

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