| CODE | SOR5122 | ||||||||||||
| TITLE | Stochastic Processes 3 | ||||||||||||
| UM LEVEL | 05 - Postgraduate Modular Diploma or Degree Course | ||||||||||||
| MQF LEVEL | 7 | ||||||||||||
| ECTS CREDITS | 10 | ||||||||||||
| DEPARTMENT | Statistics and Operations Research | ||||||||||||
| DESCRIPTION | Students taking this study-unit will be assigned a number of topics selected from the ones below which would cover topics of direct use to the particular student involved and which would make study-time demands commensurate with the number of credits being allotted: - Rigourous Definitions and Construction of Stochastic Processes; - Brownian Motion; - Martingales; - Markov Processes; - Levy Processes; - Point Processes; - Stochastic Integration. The amount of material selected and the depth and detail at which it will be dealt with will be commensurate with the credit value and the requirements needed for the student to engage effectively in related areas involved in her/his thesis. Study-Unit Aims: Stochastic Processes 3 proposes advanced topics in the theory and applications of stochastic processes for students who have achieved a certain proficiency in the area after having successfully concluded studies in Stochastic Processes 1 and 2. It goes into detail into a number of areas of contemporary importance with stochastic integration and the theory of point processes mainly in mind. Students following a number of topics with applications from stochastic processes have been kept in mind as regular consumers of this study-unit. Learning Outcomes: 1. Knowledge & Understanding: By the end of the study-unit the student will be able to: - Assemble a strong intuition of stochastic processes as an indexed collection of random variables/probability distributions invented to deal with processes which evolve probabilistically with time; - Understand how finite-dimensional distributions, a mathematical paradigm for a set of readings selected from finitely many time instants, a rigorous mathematical construct is built into a distribution over the whole ensemble of histories which project probabilistically in a consistent manner; - Follow the rationale of how path properties are analytically and measure theoretically at the foundations of a successful theory of stochastic processes; - Be familiar with a number of properties and results about some specific stochastic processes which are much in use in applications. 2. Skills: By the end of the study-unit the student will be able to: - Assimilate and interpret the theoretical assumptions underpinning the major theories in stochastic properties; - Have an appreciation for probability and statistical issues involved in the applications of stochastic processes in the various sciences, engineering and management areas; - Choose the right texts in advanced stochastic processes, with reference to mathematical or practical needs as they arise, and follow what the major results say; - Undertake stochastic modeling exercises. Main Text/s and any supplementary readings: - Shiryaev A.N., ( 1996 ) Probability, Springer. - Bauer H., ( 1981 ) Probability Theory and Elements of Measure Theory, Academic Press. - Pinsky M.A. and Karlin S. ( 2011 ) An Introduction to Stochastic Modeling, Academic Press. - Doob, J.L. ( 1953 ) Stochastic Processes, John Wiley & Sons. - Dellacherie, C., amd Meyer, P.A. Probability and Potential (1978) Vol 1, North Holland. - Williams, D. ( 2001 ) Probability with Martingales, Cambridge. - Billingsley P. ( 1995 ) Probability and Measure, John Wiley & Sons. - Chung K.L. (1990) Introduction to Stochastic Integration, Birkhauser. |
||||||||||||
| ADDITIONAL NOTES | Pre-requisite Qualification: BSc (Statistics & OR) Pre-requisite Study-units: SOR3121 |
||||||||||||
| STUDY-UNIT TYPE | Independent Study | ||||||||||||
| METHOD OF ASSESSMENT |
|
||||||||||||
| LECTURER/S | |||||||||||||
|
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. |
|||||||||||||