STAT509 APPLIED STOCHASTIC PROCESSES
| Course Code: | 2460509 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 8.0 |
| Department: | Statistics |
| Language of Instruction: | English |
| Level of Study: | Graduate |
| Course Coordinator: | Assoc.Prof.Dr. CEREN VARDAR ACAR |
| Offered Semester: | Fall Semesters. |
Course Objectives
Course Content
Markov chains, discrete and continuous Markov processes and associated limit theorems. Poison and birth and death processes. Renewal processes, martingales, Brownian motion, branching processes. Weakly and strongly stationary processes, spectral analysis. Gaussian systems.
Course Learning Outcomes
Introduction, Stochastic Processes in Science and Engineering Brownian motion: Einstein, Smoluchowski, Langevin, Ornstein and Uhlenbeck
Random processes—basic concepts, Moments of a stochastic process, stationarity and the ergodic theorem, spectral density and correlation functions, linear systems, Fluctuation-Dissipation Relation, Johnson and Nyquist.
Classification of Stochastic Processes, Chapman-Kolmogorov Equation, Master Equation , Example? One-step processes, for example?Bernoulli's Urns and Recurrence, Example?Chemical Kinetics
Exact Solutions, Moment Generating Functions, Matrix Iteration Approximation Methods, and Numerical Methods, Gillespie's Algorithm
Kolmogorov Equation, Derivation of the Fokker-Planck Equation, Macroscopic Equation, Coefficients of the Fokker-Planck Equation Pure Diffusion and Ornstein-Uhlenbeck Processes Wiener Process Ornstein-Uhlenbeck process Heuristic Picture of the Fokker-Planck Equation, Connection to Langevin Equation, Example: Kramer's Escape Problem
Limits, Mean-square continuity, stochastic differentiation, Wiener process is not differentiable. Stochastic Integration, Ito and Stratonovich Integration
Random Differential Equations, Numerical Simulation, Approximation Methods, Static Averaging (Long correlation time) Bourret's Approximation (Short correlation time) Cumulant Expansion (short correlation time) Model coefficients (arbitrary correlation time) Stochastic Delay Differential Equations