Acknowledgement

I would like to express my deep and sincere gratitude to my supervisor, Dr. Sabyasachi Bhattacharya, associate professor, Agricultural and Ecological Research Unit, Indian Statistical Institute, Kolkata. He always acted like a continuous support system during the Ph.D Research, providing several novel ideas that he never hesitated sharing. I give my deepest respect for his help and advice in about every aspect of academia. The independence, he granted me, helped me to grow as an independent researcher. I would like to thank my supervisor for providing me the best support during this five years, which is 'friendship'. Because of this we could discuss freely in many occasions regarding many aspects of life that immensely helped me to lead a healthy and better life. I am also thankful to him for giving me the opportunity to be a part of the organizational activities of national and international conferences/workshops where I learnt many things. I deeply thank him for believing in me that, I can present our research as an invited speaker in such events. This was a great moment for me and thank you for your strong support and belief on my research abilities. 

Many people have helped me not to get lost during the development of this thesis. I sincerely thank Prof. Joydev Chattopadhyay for his continuous guidance giving many new ideas. I am thankful to Dr. Yun Kang for many academic discussions that improved my understanding a lot. I am grateful to Prof. Santanu Ray for his valuable suggestions and encouragement during my Ph.D work. I sincerely acknowledge his priceless contribution on the thought of cooperation in one of my research problems. I am grateful to all of my colleagues and collaborators especially Bapi Saha, Sudip Samanta, Tridip Sardar, Joydeep Pal, Sourav Rana, Sourav Sasmal who were always together engaging me in various academic discussions that enriched my life greatly. I thank Soumalya Mukhopadhyay, santanu Biswas, Md. Saifuddin, Biman Chakraborty, Nikhil Pal for being supportive to me and their academic contributions in our research group.

Hostel life in Indian Statistical Institute played a significant role in shaping my life. During my stay I have met some of the amazing personalities in the hostel. I must thank Palash Ghosh, Buddhananda Banerjee, Abhijit Mondal, Subhajit Dutta, Nitai Debnath for helping me in various occasions. I am indebted to Sudiptada, Srikantada, Navonilda for their soulful presence around the hostel and thankful to Sudiptada for his help in many ways. I will always remember the wresting between Sandeep and Manusree, Aninditadi's understanding, Ankita's performance in drama, Kushal's smile and the super trio Parikshit, Debojyoti and Mahamitra for making the hostel life superb. Due to their soulful presence, the research life became more enjoyable. I never imagined that, Ph.D life can be so enjoyable. This is only possible because of ISI Research Scholar hostel. Thank you all for your support.

Among all the nice things, I must admit that, these long years were not always smooth. In such a moment, I visited Center for Mathematical and Statistical Sciences, Kerala to attend the summer school "Matrix Methods and Fractional Calculus". I met an amazing group of people, who made a huge impact in my life. I am indebted to Meera, Sameera, Balaswamy, Siva Kumar, Durga Prasad, Saleem, Rustam, Sonal, Sangeeta for making their presence in my life. The thought process and life style of Prof. A. M. Mathai heavily directed me and brought me back on my track. I am thankful to Prof. F. Mainardi for his help in various academic contents.

I am thankful to my teachers Vinod Berry from Presidency College, Kolkata and Prof. Aladi Subramanyam from IIT Bombay for motivating me to go for research. Without their guidance, I could not even think of going for PhD. I thank my students Guddi, Anubhab, Taniya, Dhriti who helped me to become a teacher.

Debasis, Kaushik, and Prosenjit, my dear friends, you really do not know how you have changed my life, changed my thoughts. I am really fortunate that I have met you, three people, during my lifetime. Without your support, thought process, it is impossible to become the person I am now. Kaushik taught me several lessons of life. He is the person, whom I have respected, loved, and missed the most. I certainly miss those days, when I go to Prosenjit's home to solve mathematics problems and Kakima used to cook delicious chowmin for me. I really miss it. What I believe, Debasis had left the deepest impact on all of us. He is different and I have no language to explain his impact on us. Yes, without Debasis's impact I would never choose to come back to academics. My thesis will not be complete unless I thank you all for being with me all the time.

Although it's very silly to thank parents for their support, I sincerely express gratitude for their omnipresence existence in my mind. I am fortunate to have my elder brother Pranab Kumar Bhowmick and Jaya Boudi like an umbrella on my head, who gave me the laptop to start my journey. I dedicate all my publications to my elder brother Pranab. My grandmother "chan", who at the age of ninety traveled four days by train just to be with me as a support. My younger brother Partha gave sincere effort so that, my research does not get impacted. I am fortunate to have such a wonderful family who were always with me inspiring to go for further study. To thank my wife Kavita, this page is not sufficient, this thesis is dedicated to her.