| CODE | SOR3131 | ||||||||
| TITLE | An Introduction to Stochastic Differential Equations | ||||||||
| UM LEVEL | 03 - Years 2, 3, 4 in Modular Undergraduate Course | ||||||||
| MQF LEVEL | 6 | ||||||||
| ECTS CREDITS | 4 | ||||||||
| DEPARTMENT | Statistics and Operations Research | ||||||||
| DESCRIPTION | Content: Preliminaries from measure theory and functional analysis Motivation and context for the definition of the stochastic integral The stochastic integral for Brownian motion and the Ito Formula The Ito integral in greater generality and diffusions Some important examples of SDE’s Simulation and estimation of SDE’s Study-unit Aims 1. To help student become familiar and proficient at an acceptable degree with the mathematical and probabilitistic context of stochastic differential equations; 2. to appreciate the use and modelling potential of SDEs; 3. to have some skills with dealing numerically with SDEs from the simulation and statistical angles. Learning Outcomes 1. Knowledge & Understanding: By the end of the study-unit the student will be able to: 1. Recognize contexts which necessitate the use of SDEs; 2. Appreciate the mathematical and numerical issues involved; 3. Interpret properly stochastic differential equations involved and properties known to be true in various situations. 2. Skills: By the end of the study-unit the student will be able to: 1. Apply the stochastic calculus within a theoretical context; 2. Solve the more tractable stochastic differential equations; 3. Obtain meaningful estimates of parameters of processes being fitted to given data. Main Text/s and any supplementary readings 1. Oksendal, B. (2010) Stochastic Differential Equations: An Introduction with Applications , Springer 2. E. Allen (2007) , Modeling with Itô stochastic differential equations , Springer 3. Shalizi C.R. ,Kontorovich A., (2007) Almost None of the Theory of Stochastic Processes 4. Shreve, S. (2004) Stochastic Calculus for Finance II, Springer 5. Kuo, (2006) Introduction to Stochastic Integration , Springer 6. Bain, A. (2000) Stochastic Calculus 7. Klebaner, F.C. (2005) Introdudtion to Stochastic Calculus, Imperial College Press 8. Karatzas, I. , Shreve, S. (2005) Brownian Motion and Stochastic Calculus , Springer |
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| ADDITIONAL NOTES | Pre-Requisite Study-units: SOR2120, SOR3110 Co-Requisite Study-unit: SOR3121 |
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| STUDY-UNIT TYPE | Lecture and Tutorial | ||||||||
| METHOD OF ASSESSMENT |
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| LECTURER/S | Lino Sant |
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The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
The availability of optional units may be subject to timetabling constraints. Units not attracting a sufficient number of registrations may be withdrawn without notice. It should be noted that all the information in the description above applies to study-units available during the academic year 2024/5. It may be subject to change in subsequent years. |
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