Asia in the past nurtured great civilisations and cultures, some of which withstood the onslaughts of the mighty West. After suffering from the evils of colonial rule, Asia today is poised to occupy the centre stage of the world arena, with India, China and Japan playing leading role. In this context, it is all the more necessary for college and university students in Asia and the west to acquaint themselves with the history of Asia. Hence this book. The book is different from others of this genre, as it connects the ancient and medieval Asia with the modern world. It ideals with the history of each country in its geographical setting with the interaction and impact of neighbouring countries. Early migrations, settlements, formation of kingdoms and empires, socio-economic aspects of Islamic conquests and the advent of Western powers are all accounted for. The modern period (up to 2004) is treated in a detailed manner covering topics like colonisation, impact of Western civilisation, the rise of nationalism and the achievement of independence. The current history highlights subversion of democracies, ushering in of military rule, ethnic conflicts, movements for the restoration of democracy, oppression of minorities, economic issues, nuclear proliferation and the war on terror -- all in a fascinating manner -- with maps, bibliography, and an index to stimulate reader's interest.

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 addresses 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-Pellaumail 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.