Jie Xiong - Böcker

Stochastic Filtering Theory uses probability tools to estimate unobservable stochastic processes that arise in many applied fields including communication, target-tracking, and mathematical finance.As a topic, Stochastic Filtering Theory has progressed rapidly in recent years. For example, the (branching) particle system representation of the optimal filter has been extensively studied to seek more effective numerical approximations of the optimal filter; the stability of the filter with "incorrect" initial state, as well as the long-term behavior of the optimal filter, has attracted the attention of many researchers; and although still in its infancy, the study of singular filtering models has yielded exciting results. In this text, Jie Xiong introduces the reader to the basics of Stochastic Filtering Theory before covering these key recent advances. The text is written in a style suitable for graduates in mathematics and engineering with a background in basic probability.

Since 1950 Gopinath Kallianpur has made significant contributions to the diverse area of probability and statistics, Fisher consistent estimation, non-linear prediction and filtering problems, zero-one laws for Gaussian processes, and reproducing kernel Hilbert space theory. This volume, dedicated to Kallianpur on the occasion of his 75th birthday, pays tribute to his achievements in the areas of probability and statistics, including stochastic finance.

This book examines how China’s higher vocational education (HVE) has been developed as a means of skill formation from multiple perspectives including policy, history, culture, sociology, and comparative studies (China/Canada).Through systematic analysis of relevant state policies (1980–2019), alongside empirical findings, the book reveals domestic and global policy contexts, positive and negative policy effects, and theoretical and practical policy implications for China’s skill formation through higher education reform by developing HVE to supply a high-level technically skilled workforce. Analyses and discussions are based on multiple analytical frameworks including human capital, Confucianism, neoinstitutionalism, and UNESCO’s ISCED Level 5. It concludes that China’s HVE/skill formation has been developed by mainly following the country’s distinctive political economy and history, but that it neglects the dominant local culture, which in turn has led to unsolved and newly emerged challenges impeding HVE’s high-quality development. Three policy foci are proposed for future policymaking to address such negligence. Demonstrating how China reforms, develops, and improves the higher education system to serve skill formation within the context of globalization, this book will be a valuable resource to students and scholars of vocational and technical education, comparative education, higher education, sociology of education, policy studies, and China studies.

During the last fifty years, Gopinath Kallianpur has made extensive and significant contributions to diverse areas of probability and statistics, including stochastic finance, Fisher consistent estimation, non-linear prediction and filtering problems, zero-one laws for Gaussian processes and reproducing kernel Hilbert space theory, and stochastic differential equations in infinite dimensions. To honor Kallianpur's pioneering work and scholarly achievements, a number of leading experts have written research articles highlighting progress and new directions of research in these and related areas. This commemorative volume, dedicated to Kallianpur on the occasion of his seventy-fifth birthday, will pay tribute to his multi-faceted achievements and to the deep insight and inspiration he has so graciously offered his students and colleagues throughout his career. Contributors to the volume: S. Aida, N. Asai, K. B. Athreya, R. N. Bhattacharya, A. Budhiraja, P. S. Chakraborty, P. Del Moral, R. Elliott, L. Gawarecki, D. Goswami, Y. Hu, J. Jacod, G. W. Johnson, L. Johnson, T. Koski, N. V. Krylov, I. Kubo, H.-H. Kuo, T. G. Kurtz, H. J. Kushner, V. Mandrekar, B. Margolius, R.Mikulevicius, I. Mitoma, H. Nagai, Y. Ogura, K. R. Parthasarathy, V. Perez-Abreu, E. Platen, B. V. Rao, B. Rozovskii, I. Shigekawa, K. B. Sinha, P. Sundar, M. Tomisaki, M. Tsuchiya, C. Tudor, W. A. Woycynski, J. Xiong

This book focuses on maximum principle and verification theorem for incomplete information forward-backward stochastic differential equations (FBSDEs) and their applications in linear-quadratic optimal controls and mathematical finance.  ​Lots of interesting phenomena arising from the area of mathematical finance can be described by FBSDEs. Optimal control problems of FBSDEs are theoretically important and practically relevant. A standard assumption in the literature is that the stochastic noises in the model are completely observed. However, this is rarely the case in real world situations. The optimal control problems under complete information are studied extensively. Nevertheless, very little is known about these problems when the information is not complete. The aim of this book is to fill this gap.This book is written in a style suitable for graduate students and researchers in mathematics and engineering with basic knowledge of stochastic process, optimal control and mathematical finance.