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Titlebook: Stochastic Integrals; An Introduction Heinrich Weizsäcker,Gerhard Winkler Book 1990 Springer Fachmedien Wiesbaden 1990 Approximation.Browni

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Advanced Lectures in Mathematicshttp://image.papertrans.cn/s/image/877974.jpg
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https://doi.org/10.1007/978-3-663-13923-2Approximation; Brownian motion; Differentialgleichung; Gleichung; Martingal; Martingale; Semimartingal; Sem
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The Stochastic Integral,In this chapter, we define (stochastic) Itô-integrals .H dM for local .. — martingales M and a fairly large class of adapted processes H. The integral is a random variable. It will be constructed as a suitable limit of Riemann-Stieltjes type approximations like
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Ito-Calculus,Itô’s formula is the most important tool in the theory of stochastic integration. It plays the counterpart of the fundamental theorem of classical calculus or rather its application to change of variables. It differs notably from the latter due to presence of quadratic variation.
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Change of Measures,The class of semimartingales proved to be convenient for the development of stochastic calculus because it is stable under natural operations:
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Stochastic Differential Equations,A stochastic (ordinary) differential equation (SDE) usually looks like this
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