Titlebook: Stochastic Integration and Differential Equations; Philip E. Protter Book 2005Latest edition Springer-Verlag Berlin Heidelberg 2005 Browni

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書(shū)目名稱Stochastic Integration and Differential Equations影響因子(影響力)




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書(shū)目名稱Stochastic Integration and Differential Equations被引頻次




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Semimartingales and Decomposable Processes,pted processes with left continuous, right-limited paths. Such a space of integrands suffices to establish a change of variables formula (or “It?’s formula”), and it also suffices for many applications, such as the study of stochastic differential equations. Nevertheless the space L is not general e

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General Stochastic Integration and Local Times,ess an integral as a limit of sums requires some path smoothness of the integrands and we limited our attention to processes in L, the space of adapted processes with paths that are left continuous and have right limits The space L is sufficient to prove It?’s formula, the Girsanov-Meyer Theorem, an

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General Stochastic Integration and Local Times,d processes with paths that are left continuous and have right limits The space L is sufficient to prove It?’s formula, the Girsanov-Meyer Theorem, and it also suffices in some applications such as stochastic differential equations. But other uses, such as martingale representation theory or local times, require a larger space of integrands.

嘲笑

Stochastic Differential Equations,generators of their semigroups, which are partial differential operators. Thus Feller’s investigations of diffusions (for example) were actually investigations of partial differential equations, inspired by diffusions.

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Semimartingales and Decomposable Processes, measurable functions in the theory of Lebesgue integration. Thus defining an integral as a limit of sums—which requires a degree of smoothness on the sample paths—is inadequate. In this chapter we lay the groundwork necessary for an extension of our space of integrands, and the stochastic integral is then extended in Chap. IV.

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