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Titlebook: Advances in Analysis, Probability and Mathematical Physics; Contributions of Non Sergio A. Albeverio,Wilhelm A. J. Luxemburg,Manfre Book 19

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Ultradistributions and Hyperbolicity,In this paper it is shown that every invariance principle of probability theory is equivalent to a nonstandard construction of internal S-continuous processes, which all represent — up to an infinitesimal error — the limit process. This can be applied e.g. to obtain Anderson’s nonstandard construction of a Brownian motion on a hyperfinite set.
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Extensions of Symmetric Operators,Two examples of how NSA may be useful in stochastics are considered. In Section 1 a new infinite dimensional multiplicative ergodic theorem for generalized cocycles is obtained; in Section 2 a new method of finding stationary solutions (invariant measures) to nonlinear stochastic parabolic equations is proposed.
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https://doi.org/10.1007/978-94-015-8451-7Probability theory; Variance; calculus; differential equation; mathematical physics
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978-90-481-4481-5Springer Science+Business Media B.V. 1995
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Mathematics and Its Applicationshttp://image.papertrans.cn/a/image/146659.jpg
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Theory of Elliptic Boundary Value Problems larger than the space of Schwartz distributions. As an example, we show that H. Lewy’s equation has a solution in this space whenever its right hand side is a classical smooth function or a Schwartz distribution.
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