I am studying an article which involves stochastic variables http://www.rmki.kfki.hu/~diosi/prints/1985pla112p288.pdf.(adsbygoogle = window.adsbygoogle || []).push({});

The author defines a probability distribution of a stochastic potential [itex]V[/itex] by a generator functional

[tex]

G[h] = \left<exp\left(i\int V(\vec{r},t)h(\vec{r},t)d\vec{r}dt\right)\right>,

[/tex]

where [itex]h[/itex] is an arbitrary function and [itex]\langle\rangle[/itex] stands for expectation values evaluated by means of the probabil-

ity distribution of [itex]V[/itex].

He, then equates it to (equation 1 in the article)

[tex]

G[h] = exp\left(-\frac{1}{2}\iint h(\vec{r},t)h(\vec{r}^{\prime},t)f(\vec{r}-\vec{r}^{\prime})d\vec{r}d\vec{r}^{\prime}dt\right).

[/tex]

How do we mathematically work out the steps? Any relevant reference or hint will be of great help. Thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Probability distribution of a stochastic variable

Loading...

Similar Threads for Probability distribution stochastic |
---|

I Rewriting of equality in conditional probability distribution |

I Probability of a Stochastic Markov process |

A Help with this problem of stationary distributions |

I Linear regression and probability distribution |

I Checking for Biased/Consistency |

**Physics Forums | Science Articles, Homework Help, Discussion**