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Book 2017ns such as SDE, SIE, SPDE, and others, to show not only the necessity of such theory of noncausal stochastic calculus but also its growing possibility as a tool for modeling and analysis in every domain of mathematical sciences. The reader may find there many open problems as well..音的强弱 发表于 2025-3-22 00:44:48
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Shigeyoshi OgawaIs the first book on a stochastic calculus of noncausal nature based on the noncausal stochastic integral introduced by the author in 1979.Begins with the study of fundamental properties of the noncau陶瓷 发表于 2025-3-22 14:22:15
Noncausal Calculus,We have seen in the previous chapter that the theory of Itô calculus was established after the introduction of the stochastic integral called the Itô integral and that this . integral has two important features as follows.Culpable 发表于 2025-3-22 17:41:00
Brownian Particle Equation,The Brownian particle equation, which we call . for short, is an SPDE (stochastic partial differential equation) of the first order including the white noise . as coefficients at least in its principal part.unstable-angina 发表于 2025-3-23 01:02:59
Noncausal SIE,A boundary value problem of an ordinary differential equation in a randomly disturbed situation would lead us to a stochastic integral equation of Fredholm type. In this chapter we study such an SIE in the framework of our noncausal calculus.CHARM 发表于 2025-3-23 01:52:37
Stochastic Fourier Transformation,We have seen in the previous chapter that the stochastic Fourier transformation (SFT) and the stochastic Fourier coefficients (SFCs) serve as effective tools for the study of the noncausal SIE of Fredholm type. In this chapter we shall study basic properties of these SFT and SFC.不如乐死去 发表于 2025-3-23 07:34:41
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