# DBridge: Simulation of diffusion bridge In sde: Simulation and Inference for Stochastic Differential Equations

## Description

Simulation of diffusion bridge.

## Usage

 `1` ```DBridge(x=0, y=0, t0=0, T=1, delta, drift, sigma, ...) ```

## Arguments

 `x` initial value of the process at time `t0`. `y` terminal value of the process at time `T`. `t0` initial time. `delta` time step of the simulation. `drift` drift coefficient: an expression of two variables `t` and `x`. `sigma` diffusion coefficient: an expression of two variables `t` and `x`. `T` final time. `...` passed to the `sde.sim` function.

## Details

The function returns a trajectory of the diffusion bridge starting at `x` at time `t0` and ending at `y` at time `T`.

The function uses the `sde.sim` function to simulate the paths internally. Refer to the `sde.sim` documentation for further information about the argument “`...`

## Value

 `X` an invisible `ts` object

## Author(s)

Stefano Maria Iacus

## References

Bladt, M., Soerensen, M. (2007) Simple simulation of diffusion bridges with application to likelihood inference for diffusions, mimeo.

`sde.sim`, `BBridge`
 ```1 2 3 4 5 6 7 8 9``` ```d <- expression((3-x)) s <- expression(1.2*sqrt(x)) par(mar=c(3,3,1,1)) par(mfrow=c(2,1)) set.seed(123) X <- DBridge(x=1.7,y=0.5, delta=0.01, drift=d, sigma=s) plot(X) X <- DBridge(x=1,y=5, delta=0.01, drift=d, sigma=s) plot(X) ```