Itô diffusion

An Itô diffusion solves a stochastic differential equation

d X_{t} = b (X_{t}) d t + σ (X_{t}) d B_{t}

driven by Brownian motion.

Table of contents
- Drift coefficient Itô diffusion
- Geometric Brownian motion Itô diffusion

Drift coefficient ( $b$ )

The drift coefficient is the coefficient

b

of

d t

in a stochastic differential equation. It describes the local deterministic tendency of the process.

Geometric Brownian motion ( $d X_{t} = μ X_{t} d t + σ X_{t} d B_{t}$ )

Geometric Brownian motion has the explicit strong solution

X_{t} = X_{0} exp (σ B_{t} + (μ - \frac{1}{2} σ^{2}) t) .

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