# Documentation

## Linear Drift Models

### Overview

The `SDELD` class derives from the `SDEDDO` class. These objects allow you to simulate correlated paths of `NVARS` state variables expressed in linear drift-rate form:

$d{X}_{t}=\left(A\left(t\right)+B\left(t\right){X}_{t}\right)dt+D\left(t,{X}_{t}^{\alpha \left(t\right)}\right)V\left(t\right)d{W}_{t}$

`SDELD` objects provide a parametric alternative to the mean-reverting drift form, as discussed in Example: SDEMRD Models. They also provide an alternative interface to the `SDEDDO` parent class, because you can create an object without first having to create its drift and diffusion-rate components.

### Example: SDELD Models

Create the same model as in Example: Base SDE Models:

```obj = sdeld(0, 0.1, 1, 0.3) % (A, B, Alpha, Sigma) ```
```obj = Class SDELD: SDE with Linear Drift ---------------------------------------- Dimensions: State = 1, Brownian = 1 ---------------------------------------- StartTime: 0 StartState: 1 Correlation: 1 Drift: drift rate function F(t,X(t)) Diffusion: diffusion rate function G(t,X(t)) Simulation: simulation method/function simByEuler A: 0 B: 0.1 Alpha: 1 Sigma: 0.3 ```