Real GeneralizedOrnsteinUhlenbeckProcess::variance(
Time t, Real, Time dt) const {
Real speed = speed_(t);
Volatility vol = volatility_(t);
if (speed < std::sqrt(QL_EPSILON)) {
// algebraic limit for small speed
return vol*vol*dt;
} else {
return 0.5*vol*vol/speed*(1.0 - std::exp(-2.0*speed*dt));
}
}
Animation::Animation(unsigned int rng_seed, float scale) : rng_(rng_seed), dir_(-1.0f, 1.0f), speed_(0.1f, 1.0f) {
float x = dir_(rng_);
float y = dir_(rng_);
float z = dir_(rng_);
if (std::abs(x) + std::abs(y) + std::abs(z) == 0.0f) x = 1.0f;
current_.axis = glm::normalize(glm::vec3(x, y, z));
current_.speed = speed_(rng_);
current_.scale = scale;
current_.matrix = glm::scale(glm::mat4(1.0f), glm::vec3(current_.scale));
}
Real GeneralizedOrnsteinUhlenbeckProcess::speed(Time t) const {
return speed_(t);
}
Real GeneralizedOrnsteinUhlenbeckProcess::expectation(
Time t, Real x0, Time dt) const {
return level_ + (x0 - level_) * std::exp(-speed_(t)*dt);
}
Real GeneralizedOrnsteinUhlenbeckProcess::drift(Time t, Real x) const {
return speed_(t) * (level_ - x);;
}