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To introduce the ]orward-backward stochastic differential equations (FBS- DEs, for short), let us begin with some examples. Unless otherwise speci- fled, throughout the book, we let (~, •, {Ft)t_0, P) be a complete filtered probability space on which is defined a d-dimensional standard Brownian motion W(t), such that {5~t }t_0 is the natural filtration of W(t), augmented by. | Lecture Notes in Mathematics Editors A. Dold Heidelberg E Takens Groningen B. Teissier Paris 1702 springer Berlin Heidelberg New York Barcelona Hong Kong London Milan Paris Singapore Tokyo Jin Ma Jiongmin Yong Forward-B ackward Stochastic Differential Equations and Theừ Applications .