Titlebook: Limit Theorems for Stochastic Processes; Jean Jacod,Albert N. Shiryaev Book 19871st edition Springer-Verlag Berlin Heidelberg 1987 Marting

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Convergence to a Semimartingale,limit process . also is a semimartingale; not quite an arbitrary one, though: since the method is based here on convergence of martingales and on the relations between . and its characteristics, we need these characteristics to indeed characterize the distribution. ℒ(.)of . So, in most of the chapte

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Hellinger Processes, Absolute Continuity and Singularity of Measures,years later, Hajek [80] and Feldman [53] proved a similar alternative for Gaussian measures, and several authors gave effective criteria in terms of the covariance functions or spectral quantities, for the laws of two Gaussian processes.

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Martingale Problems and Changes of Measures,compute these finite-dimensional distributions, except for PII. On the other hand, many usual processes are semimartingales; and a natural tool has emerged in Chapter II for studying them, namely their characteristics: at least, they are often easy to compute.

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Convergence of Processes with Independent Increments,firstly, the prelimiting processes, as well of course as the limiting process, have independent increments; secondly, only the limiting process has independent increments; thirdly, the limiting process itself belongs to some rather broad class of semi-martingales.

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Book 19871st editionnd stochastic integrals. Apart from a few exceptions essentially concerning diffusion processes, it is only recently that the relation between the two theories has been thoroughly studied. The authors of this Grundlehren volume, two of the international leaders in the field, propose a systematic exp

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