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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 25. Chapters: Riemann integral, It calculus, Lebesgue integration, Henstock-Kurzweil integral, Riemann-Stieltjes integral, Lebesgue-Stieltjes integration, Daniell integral, Skorokhod integral, Bochner integral, Stratonovich integral, Regulated integral, Darboux integral, Paley-Wiener integral, Russo-Vallois integral, Pfeffer integral, Homological integration, Motivic integration. Excerpt: It calculus, named after Kiyoshi It, extends the methods of calculus to stochastic processes such as Brownian motion (Wiener process). It has important applications in mathematical finance and stochastic differential equations. The central concept is the It stochastic integral. This is a generalization of the ordinary concept of a Riemann-Stieltjes integral. The generalization is in two respects. Firstly, we are now dealing with random variables (more precisely, stochastic processes). Secondly, we are integrating with respect to a non-differentiable function (technically, stochastic process). The It integral allows one to integrate one stochastic process (the integrand) with respect to another stochastic process (the integrator). It is common for the integrator to be the Brownian motion (also see Wiener process). The result of the integration is another stochastic process. In particular, the integral from to any particular is a random variable. This random variable is defined as a limit of a certain sequence of random variables. (There are several equivalent ways to construct a definition.) Roughly speaking, we are choosing a sequence of partitions of the interval from to . Then we are constructing Riemann sums. However, it is important which point in each of the small intervals is used to compute the value of the function. Typically, the left end of the interval is used. (It is conceptualized in mathematical finance as that we are first de...

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Definitions of Mathematical Integration: Riemann Integral, It Calculus, Lebesgue Integration, Henstock-Kurzweil Integral by LLC Books,LLC Books price in India is Rs. 1014 on 04th Oct 2022

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