2017 Stochastic Dynamics

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Academic unit or major
Graduate major in Systems and Control Engineering
Kimura Koji 
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Course description and aims

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.

Student learning outcomes

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

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

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

  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


None required.

Reference books, course materials, etc.

None required.

Assessment criteria and methods

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.

Related courses

  • SCE.A401 : Stochastic Systems

Prerequisites (i.e., required knowledge, skills, courses, etc.)

No prerequisites are necessary, but enrollment in the related courses is desirable.

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