# Approximated conditional law of a diffusion process by Kessler's method

### Description

Approximated conditional densities for *X(t) | X(t0) = x0* of a diffusion process.

### Usage

1 2 |

### Arguments

`x` |
vector of quantiles. |

`t` |
lag or time. |

`x0` |
the value of the process at time |

`t0` |
initial time. |

`theta` |
parameter of the process; see details. |

`log` |
logical; if TRUE, probabilities |

`d` |
drift coefficient as a function; see details. |

`dx` |
partial derivative w.r.t. |

`dxx` |
second partial derivative wrt |

`s` |
diffusion coefficient as a function; see details. |

`sx` |
partial derivative w.r.t. |

`sxx` |
second partial derivative w.r.t. |

### Details

This function returns the value of the conditional density of
*X(t) | X(t0) = x0* at point `x`

.

All the functions `d`

, `dx`

, `dxx`

, `dt`

, `s`

, `sx`

,
and `sxx`

must be functions of `t`

, `x`

, and `theta`

.

### Value

`x` |
a numeric vector |

### Author(s)

Stefano Maria Iacus

### References

Kessler, M. (1997) Estimation of an ergodic diffusion from discrete observations,
*Scand. J. Statist.*, 24, 211-229.