# Point processes in Rust
[](https://crates.io/crates/point_process)
[](https://docs.rs/point_process)
[](https://raw.githubusercontent.com/ManifoldFR/point-process-rust/master/LICENSE)
Point processes are stochastic processes with a wide range of applications in seismology, epidemiology, or financial mathematics. They are utilized to model the arrival of random events as a function of time.
This crate provides functions to simulate point processes in [Rust](https://rust-lang.org).
## Time-dependent processes
The following time-dependent point processes have been implemented:
* Poisson point process (homogeneous and inhomogeneous, with custom function)
* Hawkes processes (exponential kernel, see [@DassiosZhao13])
The API returns the process trajectories as a vector of a `struct` named `Events`, which has the following fields: a timestamp, the current process intensity and a vector holding any children events (for processes with this property, *coming soon*).
## Multidimensional processes
The crate provides the `generalized` submodule for higher-dimensional processes.
For now, only homogeneous Poisson processes have been implemented with a function
```rust
fn poisson_process(lambda: f64, domain: &T)
where T: Measurable -> ndarray::Array<f64, Ix2>
```
which takes a reference to a _measurable domain_, that is a subset of d-dimensional space that is measurable, implemented with the `Measurable` trait (see API docs), and returns a 2-dimensional array which is a set of point events in d-dimensional space falling into the domain.
## Examples
To run the examples, do for instance
```bash
cargo run --example variable_poisson
```
Some examples display a plot using [gnuplot](http://www.gnuplot.info/) with SiegeLord's [RustGnuplot](https://github.com/SiegeLord/RustGnuplot).
On Windows (see [issue here](https://github.com/SiegeLord/RustGnuplot#29)), `cargo run` is broken. You can grab a plot with:
```bash
gnuplot -p < test.gnuplot
```
The examples show how to use the API.
[@DassiosZhao13]: http://eprints.lse.ac.uk/51370/1/Dassios_exact_simulation_hawkes.pdf "Exact simulation of Hawkes process with exponentially decaying intensity"
