python 中的随机微积分库

发布于 2024-08-07 15:45:32 字数 948 浏览 7 评论 0原文

我正在寻找一个Python库，它允许我计算随机微积分的东西，比如我定义扩散的随机过程的（条件）期望。我查看了 simpy (simpy.sourceforge.net)，但它似乎不能满足我的需求。

这是为了快速原型设计和实验。在java中，我成功地使用了（现在不活动）http://martingale.berlios.de/Martingale .html 库。

这个问题本身并不困难，但是有很多重要的、样板的事情要做（有效的内存使用、变量减少技术等等）。

理想情况下，我可以写这样的东西（只是说明性的）：

def my_diffusion(t, dt, past_values, world, **kwargs):
    W1, W2 = world.correlated_brownians_pair(correlation=kwargs['rho'])
    X = past_values[-1]
    sigma_1 = kwargs['sigma1']
    sigma_2 = kwargs['sigma2']
    dX = kwargs['mu'] * X * dt + sigma_1 * W1 * X * math.sqrt(dt) + sigma_2 * W2 * X * X * math.sqrt(dt)
    return X + dX

X = RandomProcess(diffusion=my_diffusion, x0 = 1.0)
print X.expectancy(T=252, dt = 1./252., N_simul= 50000, world=World(random_generator='sobol'), sigma1 = 0.3, sigma2 = 0.01, rho=-0.1)

例如，除了在 numpy 中重新实现它之外，有人知道其他东西吗？

原文

I am looking for a python library that would allow me to compute stochastic calculus stuff, like the (conditional) expectation of a random process I would define the diffusion. I had a look a at simpy (simpy.sourceforge.net), but it does not seem to cover my needs.

This is for quick prototyping and experimentation.
In java, I used with some success the (now inactive) http://martingale.berlios.de/Martingale.html library.

The problem is not difficult in itself, but there is a lot non trivial, boilerplate things to do (efficient memory use, variable reduction techniques, and so on).

Ideally, I would be able to write something like this (just illustrative):

def my_diffusion(t, dt, past_values, world, **kwargs):
    W1, W2 = world.correlated_brownians_pair(correlation=kwargs['rho'])
    X = past_values[-1]
    sigma_1 = kwargs['sigma1']
    sigma_2 = kwargs['sigma2']
    dX = kwargs['mu'] * X * dt + sigma_1 * W1 * X * math.sqrt(dt) + sigma_2 * W2 * X * X * math.sqrt(dt)
    return X + dX

X = RandomProcess(diffusion=my_diffusion, x0 = 1.0)
print X.expectancy(T=252, dt = 1./252., N_simul= 50000, world=World(random_generator='sobol'), sigma1 = 0.3, sigma2 = 0.01, rho=-0.1)

Does someone knows of something else than reimplementing it in numpy for example ?

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