Course Overview

PRELIMINARIES
Fundamentals of real variables
Mathematical preliminaries
Fundamentals of uncertainty analysis
Fundamentals of random processes

MARTINGALES, STOPPING TIMES AND FILTRATIONS
Stochastic processes and sigma fields
Stopping times
Continuous time martingales
Reynolds transport theorem
Conservation of dissolved constituent mass

BROWNIAN MOTION
Brownian motion
Markov property
The brownian sample paths

STOCHASTIC INTEGRATION
Construction of the stochastic integral
The change-of-variable formula
Generalized ito rule for brownian motion

STOCHASTIC DIFFERENTIAL EQUATIONS (IF TIME PERMITTED)
Strong solutions
Weak solutions
Approximation methods for uncertainty analysis
Firs-order variance estimation method
Rosenblueth;s probabilistic point estimate method
Harr's probabilistic point estimate method
Li's probabilistic point estimate method

Learning Achievement

Competence

Course prerequisites

Statistics or Engineering Statistics, Calculus or Engineering Mathematics (I), or approval by the instructor

Grading Philosophy

Course schedule

Course type

Online Course Requirement

Instructor

Other information

(College of Engineering) Graduate Institute of Civil Engineering, Hydraulic Engineering Division *Majors-only (including minor and double major students).

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