# modification of a stochastic process

Let ${\{{X}_{t}\}}_{t\ge 0}$, ${\{{Y}_{t}\}}_{t\ge 0}$ be stochastic processes^{} on $(\mathrm{\Omega},\mathcal{F},P)$. ${\{{X}_{t}\}}_{t\ge 0}$ is a *modification* of ${\{{Y}_{t}\}}_{t\ge 0}$ if

$$P[\{\omega :{X}_{t}(\omega )={Y}_{t}(\omega )\}]=1$$ |

for all $t\in [0,\mathrm{\infty}).$

## References

- 1 Bernt Øksendal. , 5th ed Springer 1998.

Title | modification of a stochastic process |
---|---|

Canonical name | ModificationOfAStochasticProcess |

Date of creation | 2013-03-22 16:09:44 |

Last modified on | 2013-03-22 16:09:44 |

Owner | georgiosl (7242) |

Last modified by | georgiosl (7242) |

Numerical id | 9 |

Author | georgiosl (7242) |

Entry type | Definition |

Classification | msc 60G07 |

Classification | msc 60G05 |

Related topic | DistributionsOfAStochasticProcess |

Defines | modification |