Three Stochastic Models On Discrete Structures

To My Parents and My Sisters Acknowledgements First and above all, I praise God, the most merciful, for providing me the opportunity to step in one of the most beautiful areas in the world of science, Probability and Statistics. To be able to step strong in this way, I have also been supported by many people to whom I would like to express my sincerest gratitude. This thesis in its current form, would not have been possible without the guidance, continued support, patience and the help of my thesis advisor, Antar Bandyopadhyay. I would like to sincerely thank him for his warm encouragement, thoughtful guidance, critical comments and correction of the thesis. I am also extremely indebted to him for helping me to accomplish my research work. It has been an honor for me to be his first graduate student. I wish to express my deepest appreciation and heartfelt thanks to Rahul Roy, a truly great teacher and a wonderful person. Although I call him Rahul-da, as an elder brother, but I am grateful to him for being more like a father to me. I would like to acknowledge him not only for being an excellent teacher, but for his constructive suggestions and criticism and also for offering me valuable advice. His constant support through all stages of my stay in India, excellent care and generous invitations to his house will always remain unforgettable. Staying In India will always be an unforgettable memory since I had too many wonderful experiences. Describing my visit of India is impossible to sum up in few lines of few pages. " This is indeed India; the land of dreams and romance, of fabulous wealth and fabulous poverty, of splendor and rags, of palaces and hovels, of famine and pestilence, of genii and giants and Aladdin lamps, of tigers and elephants, the cobra and the jungle, the country of a thousand nations and a hundred tongues, of a thousand religions and two million gods, cradle of the human race, birthplace of human speech, mother of history, grandmother of legend, great-grandmother of tradition, whose yesterdays bear date with the mouldering antiquities of the rest of the nations, the one sole country under the sun that is endowed with an imperishable interest for alien prince and alien peasant, for lettered and ignorant, wise and fool, rich and poor, bond and free, the one land that all men …