Titlebook: Introduction to Stochastic Calculus; Rajeeva L. Karandikar,B. V. Rao Textbook 2018 Springer Nature Singapore Pte Ltd. 2018 Stochastic Calc

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2523-3114 - and beginning graduate-level students in the engineering and mathematics disciplines, the book is also an excellent reference resource for applied mathematicians and statisticians looking for a review of the 978-981-13-4121-2978-981-10-8318-1Series ISSN 2523-3114 Series E-ISSN 2523-3122

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Continuous Semimartingales,ly using the same techniques as in the case of SDE driven by Brownian motion. This can be done using .. The use of random time change in study of solutions to stochastic differential equations was introduced in Karandikar, pathwise stochastic calculus of continuous semimartingales, 1981, [33], Karandikar, Sankhya A, 43:121–132, 1981, [34].

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Predictable Increasing Processes,ment of the integration, we have so far suppressed another role played by predictable processes. In the decomposition of semimartingales, Theorem ., the process . with finite variation paths turns out to be a predictable process. Indeed, this identification played a major part in the development of the theory of stochastic integration.

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Integral Representation of Martingales,with respect to a given local martingale .. This result was proved by Ito’s when the underlying filtration is the filtration generated by a multidimensional Wiener process. Ito’s had proven the integral representation property for square integrable martingales and this was extended to all martingales by Clark.

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Girsanov Theorem, on ., absolutely continuous w.r.t. .. Then as noted in Remark ., . is a semimartingale on .. We will obtain a decomposition of . into . and ., where . is a .-martingale. This result for Brownian motion was due to Girsanov, and we will also present the generalizations due to Meyer.