Module sde 

Stochastic differential equations: generic SDE solver with Euler-Maruyama and Milstein methods, plus preset SDEs for common processes.

Structs

SDE

A stochastic differential equation dX = a(t,X)dt + b(t,X)dW.

SDERenderer

Render SDE solution paths with drift/diffusion visualization.

Functions

euler_maruyama

Euler-Maruyama method for solving an SDE.

heun

Heun’s method (improved Euler / predictor-corrector) for SDEs.

milstein

Milstein method for solving an SDE.

rmse

Root mean square error between two paths.

sde_cev

Constant Elasticity of Variance (CEV): dS = muSdt + sigmaS^gammadW.

sde_cir

Cox-Ingersoll-Ross: dX = kappa*(theta - X)dt + sigmasqrt(X)*dW.

sde_cir_diffusion_deriv

CIR diffusion derivative: d(sigmasqrt(x))/dx = sigma/(2sqrt(x)).

sde_gbm

Geometric Brownian Motion: dS = muSdt + sigmaSdW.

sde_gbm_diffusion_deriv

GBM diffusion derivative: d(sigma*x)/dx = sigma.

sde_langevin

Langevin equation: dV = -gammaVdt + sigma*dW (velocity process).

sde_ou

Ornstein-Uhlenbeck: dX = theta*(mu - X)dt + sigmadW.

sde_ou_diffusion_deriv

OU diffusion derivative: d(sigma)/dx = 0.

strong_error

Strong error: max |exact(t_i) - numerical(t_i)|.

weak_error

Weak error: |E[exact(T)] - E[numerical(T)]|.