## A Course in Stochastic Processes : Stochastic Models and Statistical Inference

Language: English Series: Theory and decision library | Series B: Mathematical and statistical methods ; 34 Publication details: Dordrecht Springer 1996Description: x, 351pISBN: 9780792340874 (HB)Subject(s): Distribution | Mathematical statistics | Probability | MathematicsCurrent library | Home library | Call number | Materials specified | Status | Notes | Date due | Barcode |
---|---|---|---|---|---|---|---|

IMSc Library | IMSc Library | 519.216 BOSQ (Browse shelf (Opens below)) | Not for loan | New Arrivals Displayed Till 15th October 2024 | 78188 |

Includes Bibliography (313-314) and Index

1 Basic Probability Background

2 Modeling Random Phenomena

3 Discrete - Time Markov Chains

4 Poisson Processes

5 Continuous - Time Markov Chains

6 Random Walks 7 Renewal Theory

8 Queueing Theory

9 Stationary Processes

10 ARMA model

11 Discrete-Time Martingales

12 Brownian Motion and Diffusion Processes

13 Statistics for Poisson Processes

14 Statistics of Discrete-Time Stationary Processes

15 Statistics of Diffusion Processes

This text is an Elementary Introduction to Stochastic Processes in discrete and continuous time with an initiation of the statistical inference. The material is standard and classical for a first course in Stochastic Processes at the senior/graduate level (lessons 1-12). To provide students with a view of statistics of stochastic processes, three lessons (13-15) were added. These lessons can be either optional or serve as an introduction to statistical inference with dependent observations. Several points of this text need to be elaborated, (1) The pedagogy is somewhat obvious. Since this text is designed for a one semester course, each lesson can be covered in one week or so. Having in mind a mixed audience of students from different departments (Math ematics, Statistics, Economics, Engineering, etc.) we have presented the material in each lesson in the most simple way, with emphasis on moti vation of concepts, aspects of applications and computational procedures. Basically, we try to explain to beginners questions such as "What is the topic in this lesson?" "Why this topic?", "How to study this topic math ematically?". The exercises at the end of each lesson will deepen the students' understanding of the material, and test their ability to carry out basic computations. Exercises with an asterisk are optional (difficult) and might not be suitable for homework, but should provide food for thought

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