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Full-Text Articles in Physical Sciences and Mathematics
Ito Formula And Girsanov Theorem On A New Ito Integral, Yun Peng
Ito Formula And Girsanov Theorem On A New Ito Integral, Yun Peng
LSU Doctoral Dissertations
The celebrated Ito theory of stochastic integration deals with stochastic integrals of adapted stochastic processes. The Ito formula and Girsanov theorem in this theory are fundamental results which are used in many applied fields, in particular, the finance and the stock markets, e.g. the Black-Scholes model. In chapter 1 we will briefly review the Ito theory. In recent years, there have been several extension of the Ito integral to stochastic integrals of non-adapted stochastic processes. In this dissertation we will study an extension initiated by Ayed and Kuo in 2008. In Chapter 2 we review this new stochastic integral and …
The New Stochastic Integral And Anticipating Stochastic Differential Equations, Benedykt Szozda
The New Stochastic Integral And Anticipating Stochastic Differential Equations, Benedykt Szozda
LSU Doctoral Dissertations
In this work, we develop further the theory of stochastic integration of adapted and instantly independent stochastic processes started by Wided Ayed and Hui-Hsiung Kuo in [1,2]. We provide a first counterpart to the Itô isometry that accounts for both adapted and instantly independent processes. We also present several Itô formulas for the new stochastic integral. Finally, we apply the new Itô formula to solve a linear stochastic differential equations with anticipating initial conditions.
On Moment Conditions For The Girsanov Theorem, See Keong Lee
On Moment Conditions For The Girsanov Theorem, See Keong Lee
LSU Doctoral Dissertations
In this dissertation, the well-known Girsanov Theorem will be proved under a set of moment conditions on exponential processes. Our conditions are motivated by the desire to avoid using the local martingale theory in the proof of the Girsanov Theorem. Namely, we will only use the martingale theory to prove the Girsanov Theorem. Many sufficient conditions for the validity of the Girsanov Theorem have been found since the publication of the result by Girsanov in 1960. We will compare our conditions with some of these conditions. As an application of the Girsanov Theorem, we will show the nonexistence of an …