How do we approach to dynamical problems in which identical waveforms won’t be observed and the responses of systems and structures cannot be predicted as the deterministic quantity? This course presents basic ideas for introducing probabilistic viewpoints and methods to these dynamical problems. The course will cover fundamental theory of probability and theory of stochastic processes, and focus on stochastic differential equations. We will also go over wide range of applications of stochastic dynamics.
By the end of this course, the students will be able to:
1) Understand the basic concepts of stochastic dynamics
2) Learn the probabilistic approach to random or uncertain phenomena
3) Acquire knowledge of stochastic differential equations
Probabilistic Viewpoint, Stochastic Dynamics, Stationarity and Nonstationarity, Markov Process, Wiener Process, Stochastic Differential Equations,
Stochastic Response Analysis
|✔ Specialist skills||Intercultural skills||Communication skills||Critical thinking skills||Practical and/or problem-solving skills|
At the beginning of each class, the points of the previous class are reviewed. Towards the end of class, the subjects planned on that day will be explained and discussed.
|Course schedule||Required learning|
|Class 1||Introduction to Stochastic Dynamics －Probabilistic viewpoint, Random phenomena, Uncertain system||Probabilistic viewpoint|
|Class 2||Probability Theory －Probability space, Random Variable, Moments, Convergence, Conditional Expectation||Understanding of probability and random variables|
|Class 3||Stochastic Processes －Basic concepts, Moment function, Stationary process, Mean square calculus||Basic concepts of stochastic processes|
|Class 4||Stochastic Processes －Markov process, Independent increment process, Wiener process, White noise||Classification of stochastic processes|
|Class 5||Stochastic Processes －Kinetic equation, Fokker-Planck equation||Derivation of Fokker-Planck equation|
|Class 6||Stochastic Processes －Diffusion process||Basic concepts of diffusion process|
|Class 7||Stochastic Differential Equations －SDE and its solutions, Stochastic integral||Concepts of stochastic integral|
|Class 8||Stochastic Dynamics －Stochastic dynamics in various research fields||Stochastic dynamics in various research fields|
1) Students will be assessed on understanding of the basic theory and its application associated with stochastic dynamics.
2) Grades will be evaluated based on exercise problems and course reports.
No prerequisites are necessary, but enrollment in the related courses is desirable.