Han, Xiaoying, Kloeden, Peter E. 　著

目次

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 Itô 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.