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Introduction to stochastic calculus

Karandikar, Rajeeva L.

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Introduction to stochastic calculus

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Introduction to stochastic calculus/ by Rajeeva L. Karandikar, B. V. Rao.
作者:	Karandikar, Rajeeva L.
其他作者:	Rao, B. V.
出版者:	Singapore :Springer Singapore : : 2018.,
面頁冊數:	xiii, 441 p. :digital ;24 cm.
內容註:	Discrete Parameter Martingales -- Continuous Time Processes -- The Ito Integral -- Stochastic Integration -- Semimartingales -- Pathwise Formula for the Stochastic Integral -- Continuous Semimartingales -- Predictable Increasing Processes -- The Davis Inequality -- Integral Representation of Martingales -- Dominating Process of a Semimartingale -- SDE driven by r.c.l.l. Semimartingales -- Girsanov Theorem.
Contained By:	Springer eBooks
標題:	Stochastic processes. -
電子資源:	http://dx.doi.org/10.1007/978-981-10-8318-1
ISBN:	9789811083181

Introduction to stochastic calculus
Karandikar, Rajeeva L.

Introduction to stochastic calculus[electronic resource] /by Rajeeva L. Karandikar, B. V. Rao. - Singapore :Springer Singapore :2018. - xiii, 441 p. :digital ;24 cm. - Indian statistical institute series,2523-3114. - Indian statistical institute series..

Discrete Parameter Martingales -- Continuous Time Processes -- The Ito Integral -- Stochastic Integration -- Semimartingales -- Pathwise Formula for the Stochastic Integral -- Continuous Semimartingales -- Predictable Increasing Processes -- The Davis Inequality -- Integral Representation of Martingales -- Dominating Process of a Semimartingale -- SDE driven by r.c.l.l. Semimartingales -- Girsanov Theorem.

This book sheds new light on stochastic calculus, the branch of mathematics that is most widely applied in financial engineering and mathematical finance. The first book to introduce pathwise formulae for the stochastic integral, it provides a simple but rigorous treatment of the subject, including a range of advanced topics. The book discusses in-depth topics such as quadratic variation, Ito formula, and Emery topology. The authors briefly address continuous semi-martingales to obtain growth estimates and study solution of a stochastic differential equation (SDE) by using the technique of random time change. Later, by using Metivier-Pellumail inequality, the solutions to SDEs driven by general semi-martingales are discussed. The connection of the theory with mathematical finance is briefly discussed and the book has extensive treatment on the representation of martingales as stochastic integrals and a second fundamental theorem of asset pricing. Intended for undergraduate- 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 topic.

ISBN: 9789811083181

Standard No.: 10.1007/978-981-10-8318-1doiSubjects--Topical Terms:

520663
Stochastic processes.

LC Class. No.: QA274 / .K373 2018

Dewey Class. No.: 519.23

Introduction to stochastic calculus
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505 0 $a Discrete Parameter Martingales -- Continuous Time Processes -- The Ito Integral -- Stochastic Integration -- Semimartingales -- Pathwise Formula for the Stochastic Integral -- Continuous Semimartingales -- Predictable Increasing Processes -- The Davis Inequality -- Integral Representation of Martingales -- Dominating Process of a Semimartingale -- SDE driven by r.c.l.l. Semimartingales -- Girsanov Theorem.
520 $a This book sheds new light on stochastic calculus, the branch of mathematics that is most widely applied in financial engineering and mathematical finance. The first book to introduce pathwise formulae for the stochastic integral, it provides a simple but rigorous treatment of the subject, including a range of advanced topics. The book discusses in-depth topics such as quadratic variation, Ito formula, and Emery topology. The authors briefly address continuous semi-martingales to obtain growth estimates and study solution of a stochastic differential equation (SDE) by using the technique of random time change. Later, by using Metivier-Pellumail inequality, the solutions to SDEs driven by general semi-martingales are discussed. The connection of the theory with mathematical finance is briefly discussed and the book has extensive treatment on the representation of martingales as stochastic integrals and a second fundamental theorem of asset pricing. Intended for undergraduate- 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 topic.
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