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Titlebook: Limit Theorems for Stochastic Processes; Jean Jacod,Albert N. Shiryaev Book 2003Latest edition Springer-Verlag GmbH Germany 2003 Convergen

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Characteristics of Semimartingales and Processes with Independent Increments,We continue across our project of expounding the general theory of processes. However, here we touch upon a slightly different aspect of the theory, which at the same time is much less widely known than what was in the first chapter. This is also the aspect which will be most directly useful for limit theorems.
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Contiguity, Entire Separation, Convergence in Variation,We examine here two apparently disconnected sorts of problems. The relation between them essentially comes from the fact that, in order to solve both of them, we use the same tool, namely the Hellinger processes introduced in the previous chapter.
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Limit Theorems, Density Processes and Contiguity,Let us roughly describe the problems which will retain our attention in this last chapter.
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Convergence to a Process with Independent Increments,., .., ..), and a limiting process . which is a PII with characteristics (., ., .). Our main objective is to prove that the various conditions of Chapter VII still insure the (functional or finite-dimensional) convergence of (..) to ., although the ... are no longer PII.
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https://doi.org/10.1007/978-3-662-05265-5Convergence of processes; Martingale; Semimartingale; Semimartingales; Stochastic integrals; Stochastic p
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978-3-642-07876-7Springer-Verlag GmbH Germany 2003
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