Probability & Statistical Inference · Stochastic Processes

Stochastic processes · Continuous-time Markov chains

Public introduction · full guide in Eikos

Introduction

What this guide covers

Introduction Introduction Advanced stochastic processes

Overview

Topics covered

  • Introduction
  • Continuous Time Markov Chains
  • Fundamentals of continuous time and the Markov property
  • Temporal homogeneity
  • The Chapman-Kolmogorov equations
  • Dwell times and the embedded jump chain

Related concepts

Main connections

  • Linear algebra & matrices
  • Calculus & differentiation
  • Poisson distribution
  • Markov chain Monte Carlo (MCMC)
  • Mean & expected value
  • Variance & standard deviation

Compatible notation

Mathematical sample in LaTeX

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

ℙ(X(t+s)=j|X(s)=i,X(tn)=in,…,X(t1)=i1)=ℙ(X(t+s)=j|X(s)=i).
View LaTeX source\P\big(X(t+s) = j \;\big|\; X(s) = i, X(t_n) = i_n, \dots, X(t_1) = i_1\big) = \P\big(X(t+s) = j \;\big|\; X(s) = i\big).