Advanced & Applied Topics · Simulation & Monte Carlo Methods

Simulation: generation of random vectors and stochastic processes

Public introduction · full guide in Eikos

Introduction

What this guide covers

A mathematical and algorithmic reference for the numerical simulation of multidimensional structures, nonlinear transformations, Poisson, Wiener, Ornstein-Uhlenbeck processes and Markov chain schemes.

Overview

Topics covered

  • Introduction
  • Random Vector Generation and Stochastic Processes
  • Random Vector Fundamentals
  • Moments of a Random Vector
  • Generation of the Multinormal Distribution
  • 2.1 The Cholesky Decomposition Method

Related concepts

Main connections

  • Linear algebra & matrices
  • Poisson distribution
  • Normal (Gaussian) distribution
  • Mean & expected value
  • Variance & standard deviation
  • Quantiles & percentiles

Compatible notation

Mathematical sample in LaTeX

The expression is rendered accessibly, with its LaTeX source preserved below.

𝐱=𝛍+𝐋𝐳
View LaTeX source\mathbf{x} = \boldsymbol{\mu} + \mathbf{L}\mathbf{z}