Gaussian increment with variance proportional to time

Read the equation

Multiplying a standard normal draw by √dt gives a zero-mean Gaussian increment of variance dt. This is the increment distribution used in Wiener-driven discretizations. The function’s callback must supply an independent standard normal draw and dt must be nonnegative; the callback type itself does not enforce either assumption.

Terms & definitions

How it works

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Original context

// ═══════════════════════════════════════════════════════════════════════════════
// STOCHASTIC CALCULUS EQUATIONS
// ═══════════════════════════════════════════════════════════════════════════════

// WienerProcess generates Wiener increment dW ~ N(0, dt)
func WienerProcess(dt float64, rng func() float64) float64 {
	// dW = √dt · Z where Z ~ N(0,1)
	return math.Sqrt(dt) * rng()
}

// ItoProcess computes dX = μ·dt + σ·dW (Ito SDE step)
func ItoProcess(x, mu, sigma, dt, dw float64) float64 {
	return x + mu*dt + sigma*dw
}

// OrnsteinUhlenbeck computes mean-reverting process
// dX = θ(μ - X)dt + σdW

dW = √dt · Z where Z ~ N(0,1)

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