A NEW THEORY OF STOCHASTIC INTEGRATION

This dissertation would not be possible without many valuable contributions. First of all, I would like to express my deep gratefulness and indebtedness to my dis-sertation advisor, Professor Hui-Hsiung Kuo, for his help, guidance and support. In particular, I really appreciate the consideration and patience he has had with me throughout these years. He is not only an outstanding researcher but he is also an excellent teacher. He always encourages students to do their best and concerns about the students ’ understanding. It was absolutely my great pleasure to be a student under his supervision. I would also like to thank Professors William Adkins, Mark Davidson, Richard Litherland, Padmanabhan Sundar, and Martin Tzanov for their kindness on serv-ing as my final examination committee members. My thanks also go to the faculty and staff members in the LSU Department of Mathemetics for their help and very warm environment during my whole time at LSU. I thank all my fellow graduate students for a plenty of mathematical discussions, some useful ideas and their help. I would like to give my deepes