Read the equation
This relation defines @brief Ornstein-Uhlenbeck step: dX in the source section “Ornstein-Uhlenbeck step: dX = θ(μ - X)dt + σdW · @brief Ornstein-Uhlenbeck step: dX”. It specifies the displayed relationship between the named quantities or parameters. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an unprovided physical or cognitive meaning to them.
Terms & definitions
The recovered passage does not supply a separate symbol table. Read the source context for the notation used in this version; familiar letters may carry different meanings in other builds.
How it works
Read @brief Ornstein-Uhlenbeck step: dX as the quantity being defined or updated by this relation.
Substitute the source-defined variables or recorded values and follow the displayed arithmetic and indexing exactly.
Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.
Assumptions & limits
This source expression was recovered from the pinned code revision. Its presence does not establish that the associated program was built, run, or scientifically validated.
Original context
Read the surrounding source passage
* @brief Itô SDE step: dX = μdt + σdW
*/
inline double ito_step(double x, double drift, double diffusion, double dW, double dt) {
return x + drift * dt + diffusion * dW;
}
/**
* @brief Ornstein-Uhlenbeck step: dX = θ(μ - X)dt + σdW
*/
inline double ou_step(double x, double theta, double mu, double sigma, double dW, double dt) {
return x + theta * (mu - x) * dt + sigma * dW;
}
/**
* @brief Langevin dynamics step: dX = -∇V(X)dt + √(2T)dW
*/
inline double langevin_step(double x, double gradient, double temperature, double dW, double dt) {
return x - gradient * dt + std::sqrt(2.0 * temperature) * dW;Exact original notation
@brief Ornstein-Uhlenbeck step: dX = θ(μ - X)dt + σdW