Probability & Statistical Inference · Stochastic Processes

Stochastic processes: Brownian motion and related processes

Public introduction · full guide in Eikos

Introduction

What this guide covers

Rigorous analysis of non-differentiable continuous trajectories, the Itô calculus and probabilistic modeling of systems with diffusion.

Overview

Topics covered

  • Introduction
  • Brownian Motion and Related Processes
  • 1. Fundamentals of Stochastic Processes
  • 1.1 Definition and Theoretical Construction
  • 1.2 Leaks, Stop Times and Martingales
  • 2. Brownian Motion (Wiener Process)

Related concepts

Main connections

  • Calculus & differentiation
  • Mean & expected value
  • Variance & standard deviation
  • Mathematical expectation & moments
  • Normal (Gaussian) distribution
  • Conditional probability & independence

Compatible notation

Mathematical sample in LaTeX

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

X={Xt:t∈T}
View LaTeX sourceX = \{X_t : t \in T\}