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# 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
```