Sudip Sinha | Louisiana State University (original) (raw)
Papers by Sudip Sinha
This dissertation results from a culmination of years of effort, help from many people, a robust ... more This dissertation results from a culmination of years of effort, help from many people, a robust support system, and love for knowledge. I would like to express heartfelt gratitude to my advisors-Professors Hui-Hsiung Kuo and Padmanabhan Sundar. Without their timely guidance, encouragement, patience, kindness, empathy, and unwavering support, I would not be where I am today. I shall strive to uphold the strong work ethic that I have witnessed in them. I would also like to thank Professors Ambar Sengupta and Gerry Knapp for serving on my advisory committee. I am honored that Pujan Shrestha chose to work with me throughout the doctoral journey. Having a colleague with whom I could work in tandem made me cherish my time here. I am thankful to him for being patient with my mathematical ramblings, research discussions, and bringing me out of procrastination loops. I am indebted to my master's thesis advisor Professor Fabio Antonelli. It is from him that I started to understand and appreciate mathematics for what it is. His teaching and advice motivated me to pursue research in stochastic analysis. I also want to thank Professors Davide Gabrielli, Ida Germana Minelli, and Prasanna Kumar for teaching me and supporting my endeavors. I am grateful to Professor Jeffrey Roland for helping me explore the foundations and philosophies of mathematics and to Professor James Oxley for helping me refine my communication techniques. I thank Professors Shipman, Adkins, Dasbach, and the other professors and graduate students for creating a lively and healthy environment conducive to research. None of this would have been possible without a sturdy support system. I am grateful to my family for their unconditional love and support. I would like to thank Bree, Kaju, Jessica, Rachel, Steven, Irfan, Liem, Huy, and all my friends who made living in Baton Rouge an enjoyable experience. My heartfelt gratitude to Ankan and Anirudh for lively discussions on mathematics, the universe, and everything. I am grateful to Tuppu for being a constant source of love, support, and inspiration. Finally, my work builds on the mathematical framework laid by mathematicians and philosophers over millennia of painstaking effort. Quoting Isaac Newton, "If I have seen further, it is by standing on the shoulders of giants." v
The primary goal of this paper is to prove a near-martingale optional stopping theorem and establ... more The primary goal of this paper is to prove a near-martingale optional stopping theorem and establish solvability and large deviations for a class of anticipating linear stochastic differential equations. We prove the existence and uniqueness of solutions using two approaches: (1) Ayed-Kuo differential formula using an ansatz, and (2) a novel braiding technique by interpreting the integral in the Skorokhod sense. We establish a Freidlin-Wentzell type large deviations result for solution of such equations.
Stochastic differential equations with adapted integrands and initial conditions are well studied... more Stochastic differential equations with adapted integrands and initial conditions are well studied within Itô’s theory. However, such a general theory is not known for corresponding equations with anticipation. We use examples to illustrate essential ideas of the Ayed–Kuo integral and techniques for dealing with anticipating stochastic differential equations. We prove the general form of the solution for a class of linear stochastic differential equations with adapted coefficients and anticipating initial condition, which in this case is an analytic function of a Wiener integral. We show that for such equations, the conditional expectation of the solution is not the same as the solution of the corresponding stochastic differential equation with the initial condition as the expectation of the original initial condition. In particular, we show that there is an extra term in the stochastic differential equation, and give the exact form of this term.
Civil War Book Review, 2018
Journal of Stochastic Analysis, 2021
Fecha de envío: 01/12/2021 Fecha de aceptación:10/12/2021 El "acompañamiento" como modelo para el... more Fecha de envío: 01/12/2021 Fecha de aceptación:10/12/2021 El "acompañamiento" como modelo para el impulso y la gestión de
This dissertation results from a culmination of years of effort, help from many people, a robust ... more This dissertation results from a culmination of years of effort, help from many people, a robust support system, and love for knowledge. I would like to express heartfelt gratitude to my advisors-Professors Hui-Hsiung Kuo and Padmanabhan Sundar. Without their timely guidance, encouragement, patience, kindness, empathy, and unwavering support, I would not be where I am today. I shall strive to uphold the strong work ethic that I have witnessed in them. I would also like to thank Professors Ambar Sengupta and Gerry Knapp for serving on my advisory committee. I am honored that Pujan Shrestha chose to work with me throughout the doctoral journey. Having a colleague with whom I could work in tandem made me cherish my time here. I am thankful to him for being patient with my mathematical ramblings, research discussions, and bringing me out of procrastination loops. I am indebted to my master's thesis advisor Professor Fabio Antonelli. It is from him that I started to understand and appreciate mathematics for what it is. His teaching and advice motivated me to pursue research in stochastic analysis. I also want to thank Professors Davide Gabrielli, Ida Germana Minelli, and Prasanna Kumar for teaching me and supporting my endeavors. I am grateful to Professor Jeffrey Roland for helping me explore the foundations and philosophies of mathematics and to Professor James Oxley for helping me refine my communication techniques. I thank Professors Shipman, Adkins, Dasbach, and the other professors and graduate students for creating a lively and healthy environment conducive to research. None of this would have been possible without a sturdy support system. I am grateful to my family for their unconditional love and support. I would like to thank Bree, Kaju, Jessica, Rachel, Steven, Irfan, Liem, Huy, and all my friends who made living in Baton Rouge an enjoyable experience. My heartfelt gratitude to Ankan and Anirudh for lively discussions on mathematics, the universe, and everything. I am grateful to Tuppu for being a constant source of love, support, and inspiration. Finally, my work builds on the mathematical framework laid by mathematicians and philosophers over millennia of painstaking effort. Quoting Isaac Newton, "If I have seen further, it is by standing on the shoulders of giants." v
The primary goal of this paper is to prove a near-martingale optional stopping theorem and establ... more The primary goal of this paper is to prove a near-martingale optional stopping theorem and establish solvability and large deviations for a class of anticipating linear stochastic differential equations. We prove the existence and uniqueness of solutions using two approaches: (1) Ayed-Kuo differential formula using an ansatz, and (2) a novel braiding technique by interpreting the integral in the Skorokhod sense. We establish a Freidlin-Wentzell type large deviations result for solution of such equations.
Stochastic differential equations with adapted integrands and initial conditions are well studied... more Stochastic differential equations with adapted integrands and initial conditions are well studied within Itô’s theory. However, such a general theory is not known for corresponding equations with anticipation. We use examples to illustrate essential ideas of the Ayed–Kuo integral and techniques for dealing with anticipating stochastic differential equations. We prove the general form of the solution for a class of linear stochastic differential equations with adapted coefficients and anticipating initial condition, which in this case is an analytic function of a Wiener integral. We show that for such equations, the conditional expectation of the solution is not the same as the solution of the corresponding stochastic differential equation with the initial condition as the expectation of the original initial condition. In particular, we show that there is an extra term in the stochastic differential equation, and give the exact form of this term.
Civil War Book Review, 2018
Journal of Stochastic Analysis, 2021
Fecha de envío: 01/12/2021 Fecha de aceptación:10/12/2021 El "acompañamiento" como modelo para el... more Fecha de envío: 01/12/2021 Fecha de aceptación:10/12/2021 El "acompañamiento" como modelo para el impulso y la gestión de