Titlebook: Schrödinger Equations and Diffusion Theory; Masao Nagasawa Book 1993 Springer Basel AG 1993 chaos.diffusion process.probability.probabilit

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Masao Nagasawa, Software as a service and Business-to-Business client rela.Exploring the Cloud Computing (CC) commercial landscape as it matures; this book asserts that the key ingredient in sustaining the Software as a Service (SaaS) business model is subscription renewal. Chronicling the evolution and future tr

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,Equivalence of Diffusion and Schrödinger Equations,rmula, one can regard Theorem 4.1 as an assertion on transformations between partial differential equations of different types. Referring to the Appendix is recommended in connection with the theme of this chapter.

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,The Schrödinger Equation can be a Boltzmann Equation,r case we take the creation and killing . = -.ϕ/ϕ induced by ϕ(.), and another function . such that ., and moreover assume the admissibility condition (5.12) so that . is the Csiszar projection of .. This case occurs, if a solution .= . of the Schrödinger equation is given beforehand and if we define Õ = . and . in terms of . and .=

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Diffusion Processes and their Transformations,n the following chapters. Moreover, transformations of diffusion processes by means of multiplicative functionals, a renormalization of Kac’s semi-groups, and Feller’s one-dimensional diffusion processes will be explained.

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Duality and Time Reversal of Diffusion Processes,be applied to time-inhomogeneous diffusion processes in the third and fourth sections. Moreover, two different representations of a diffusion process will be established. They will play a crucial role in connection with quantum mechanics in Chapter 4.

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,Equivalence of Diffusion and Schrödinger Equations, role in this chapter. One of the consequences is the duality formula, especially (3.35′), which will be renumbered as (4.7). Accepting the duality formula, one can regard Theorem 4.1 as an assertion on transformations between partial differential equations of different types. Referring to the Appen

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