Random Ordinary Differential Equations and Their Numerical Solution

Preface.- Reading Guide.- Part I Random and Stochastic Ordinary Differential Equations.- 1.Introduction.-. 2.Random ordinary differential equations.- 3.Stochastic differential equations.- 4.Random dynamical systems.- 5.Numerical dynamics.- Part II Taylor Expansions.- 6.Taylor expansions for ODEs and SODEs.- 7.Taylor expansions for RODEs with affine noise.- 8.Taylor expansions for general RODEs.- Part III Numerical Schemes for Random Ordinary Differential Equations.- 9.Numerical methods for ODEs and SODEs.- 10.Numerical schemes: RODEs with Ito noise.- 11.Numerical schemes: affine noise.- 12.RODE-Taylor schemes.- 13.Numerical stability.- 14.Stochastic integrals.- Part IV Random Ordinary Differential Equations in the Life Sciences.- 15.Simulations of biological systems.- 16.Chemostat.- 17.Immune system virus model.- 18.Random Markov chains.- Part V Appendices.- A.Probability spaces.- B.Chain rule for affine RODEs.- C.Fractional Brownian motion.- References.- Index.

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• Matemática aplicada
• Cálculo diferencial e equações
• Probabilidade e Estatística
• Estocástica
• Análise numérica
• Ciências da vida: temas gerais

37H10, 60H10, 60H35;34F05, 37H70, 60H30, 65LC30, 65L05, 65L06, 65L20, 92-08;random dynamical systems;biological sciences;Numerical Schemes for RODEs;Taylor expansions for ODEs and SODEs;Stochastic Ordinary Differential Equations;Life Sciences;ordinary differential equations