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- W4233549181 abstract "This chapter discusses basic mathematical concepts, Stochastic integrals, Ito's integral, Ito's formula, and martingale representation, used in Stochastic differential equations. It looks at a specialized mathematical apparatus that directly exploits the random nature of Brownian motion (BM). Specifically, it considers Ito stochastic integral defined with respect to BM and defines the class of admissible functions or processes to which the Ito integral will be applied. To correctly evaluate Ito stochastic integrals, the chapter uses what is called the Ito chain rule or Ito formula. The Ito integral is a martingale with respect to At. The chapter argues that any square-integrable random variable that is measurable with respect to a BM is representable as a stochastic integral in terms of this BM. In particular, any martingale that is adapted to a BM filtration can be written as a stochastic integral." @default.
- W4233549181 created "2022-05-12" @default.
- W4233549181 date "2017-03-15" @default.
- W4233549181 modified "2023-10-17" @default.
- W4233549181 title "Mathematical Foundations 4" @default.
- W4233549181 doi "https://doi.org/10.1002/9781119377399.ch4" @default.
- W4233549181 hasPublicationYear "2017" @default.
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