SKU/Artículo: AMZ-B09JXZTJ5N
Newton's Method for Stochastic Differential Equations: From a Heuristic Algorithm Formulation to the Second-Order Convergence
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- Starting from a heuristic formulation of Newton's method for stochastic differential equations (Chapter 1), we show that a modified Milstein scheme (Chapter 3) combined with explicit Newton's method (Chapter 4) enables us to construct fast converging sequences of approximate solutions of stochastic differential equations (Chapter 5). The fast uniform convergence of our Newton-Milstein scheme follows from Amano's probabilistic second-order error estimate, which had been an open problem since 1991. The Newton-Milstein scheme, which is based on a modified Milstein scheme (Chapter 3) and the symbolic Newton's method (Chapter 4), will be classified as a numerical and computer algebraic hybrid method, and it may give a new possibility to the study of computer algebraic method in stochastic analysis (Chapters 1 and 5).
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