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- W85201719 abstract "Publisher Summary This chapter discusses nonlinear equations in abstract spaces. Although basic laws generally lead to nonlinear differential and integral equations in many areas, linear approximations are usually employed for mathematical tractability and the use of superposition. Where nonlinear systems must be solved, perturbation theory is classically used which can be a severe restriction. A further substantial difficulty is that real systems generally involve uncertainties and fluctuations and are consequently to be considered as stochastic system. The objective then must be to consider nonlinear stochastic systems to allow more realistic modeling. Earlier papers have studied objectives, limitations, and necessary restrictive assumptions for the various methods for solution of linear stochastic differential equations arising in physical problems. An iterative procedure was developed using the concept of stochastic Green's functions and allowing treatment of a wide class of problems without many of the limitations inherent in other methods or restrictive assumptions involving highly special processes." @default.
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- W85201719 date "1978-01-01" @default.
- W85201719 modified "2023-10-16" @default.
- W85201719 title "NEW RESULTS IN STOCHASTIC EQUATIONS - THE NONLINEAR CASE" @default.
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- W85201719 doi "https://doi.org/10.1016/b978-0-12-434160-9.50006-0" @default.
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