Stochastic Processes

MATH27712 Stochastic Processes 10 Semester 2 Undergraduate Level 2 Goran Peskir Unit coordinator Department of Mathematics 1 FHEQ level (Framework for Higher Education Qualifications) ' Middle part of Bachelors ' European Credit Transfer & Accumulation System Rating : 5.0 A stochastic process is a collection of random variables that describe the progression of a non-deterministic system as a function of time.Stochastic processes are used as modelling tools within a wide range of applications arising virtually in any area of modern science and engineering where randomness plays a role.The unit aims to present the most important classes of stochastic processes by focusing on the fundamental examples, describing the meaning of their sample paths, and explaining their role in modelling specific science and/or engineering phenomena.These classes of stochastic processes are of fundamental interest in (i) Mathematical Finance, (ii) Actuarial Science, and (iii) Statistics, in addition to being of interest in themselves as fundamental entities of modern (iv) Probability Theory that provide fascinating connections to (v) Mathematical Analysis.Syllabus: (with approximate times) 1. Introduction (stochastic process, sample path, increment, marginal     law, first entry time) [1 week] 2. Random walk (definition, basic properties, marginal law, examples     of application) [3 weeks] 3. Poisson process (definition, basic properties, marginal law, examples     of application) [3 weeks]  4. Wiener process [Brownian motion] (definition, basic properties, marginal     law, examples of application) [3 weeks]  5. Stationary process (definition, covariance function, examples of     application) [1 week]    A stochastic process is a collection of random variables that describe the progression of a non-deterministic system as a function of time.Stochastic processes are used as modelling tools within a wide range of applications arising virtually in any area of modern science and engineering where randomness plays a role.The unit aims to present the most important classes of stochastic processes by focusing on the fundamental examples, describing the meaning of their sample paths, and explaining their role in modelling specific science and/or engineering phenomena.These classes of stochastic processes are of fundamental interest in (i) Mathematical Finance, (ii) Actuarial Science, and (iii) Statistics, in addition to being of interest in themselves as fundamental entities of modern (iv) Probability Theory that provide fascinating connections to (v) Mathematical Analysis.Syllabus: (with approximate times) 1. Introduction (stochastic process, sample path, increment, marginal     law, first entry time) [1 week] 2. Random walk (definition, basic properties, marginal law, examples     of application) [3 weeks] 3. Poisson process (definition, basic properties, marginal law, examples     of application) [3 weeks]  4. Wiener process [Brownian motion] (definition, basic properties, marginal     law, examples of application) [3 weeks]  5. Stationary process (definition, covariance function, examples of     application) [1 week]    The unit aims to:- Present the most important classes of Stochastic Processes by focusing on the fundamental examples, describing the meaning of their sample paths, and explaining their role in modelling specific science and/or engineering phenomena;- Provide an overview of Stochastic Processes and explain what the students can expect in related directions from the probability-based units in year 3, 4 and beyond.   <ul> <li>Define a stochastic process and describe its meaning as a modelling tool of a specific science/engineering phenomenon.</li> <li>Describe the structure of the sample paths of a stochastic process and derive their basic properties.</li> <li>Derive the marginal law of a stochastic process, calculate its expectation/variance, and study its asymptotic behaviour.</li> <li>Define the first entry time of a stochastic process and apply the derived results in a variety of applied settings.</li></ul> 1 Written exam 100% Summer exam     2 hours    General feedback provided after exam is marked.      MATH11711 Probability I Pre-Requisite Compulsory MATH27720 Probability and Statistics 2 Co-Requisite Compulsory MATH27712 Co-Requisite: Students must be enrolled on MATH27720 in order to enrol onto MATH27712 N Stochastic processes    Bass, Richard F., author.    Cambridge University Press    2011    ISBN: 9780511997044 Stochastic processes : an introduction    Jones, P. W.    CRC Press Taylor & Francis Group    2018    ISBN: 9781498778114 A first course in stochastic processes    Karlin, Samuel, 1924-2007, author.    Academic Press    1975    ISBN: 9780080570419 Lectures 11 Practical classes & workshops 11 0 78