Skip to main content
Engineering LibreTexts

8: Stochastic Simulation

  • Page ID
    47265
    • Franz S. Hover & Michael S. Triantafyllou
    • Massachusetts Institute of Technology via MIT OpenCourseWare
    \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    • 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.


    This page titled 8: Stochastic Simulation is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Franz S. Hover & Michael S. Triantafyllou (MIT OpenCourseWare) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.