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8: Stochastic Simulation

Last updated

Apr 23, 2021
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- 7.8: Solving Dynamic Programming on a Computer
- 8.1: Introduction to Stochastic Simulation

Franz S. Hover & Michael S. Triantafyllou
Massachusetts Institute of Technology via MIT OpenCourseWare

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8.1: Introduction to Stochastic Simulation
Overview of stochiastic processes and the chapter's focus on random static variables, as they apply to robotic systems.
8.2: Monte Carlo Simulation
Introduction to the Monte Carlo simulation as a method of predicting outcome probability when there is interference from random variables.
8.3: Making Random Numbers
Generating random numbers from an underlying random distribution, to be used in creating the samples of a given distribution that the Monte Carlo simulation requires.
8.4: Grid-Based Techniques
Grid-based techniques: treating calculations on the output variable as an integral over the domain of random variables. Includes use of the trapezoid rule, in one and two dimensions; introduction to Hermite polynomials and their use with the Gaussian pdf to create easily integrated orthagonal polynomials.
8.5: Issues of Cost and Accuracy
Comparison of the Monte Carlo simulation, trapezoid rule, and Gauss-Hermite quadrature as techniques for integration, in terms of accuracy and evaluation cost.

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