# Martingale criterion (continuous time)

###### Theorem 1.

Let $X$ be a local martingale^{}. Then $X$ is a continuous^{} martingale^{} iff the set $\mathrm{\{}{X}_{\tau}\mathrm{:}\tau \mathit{}\mathit{\text{stopping time}}\mathrm{,}\tau \mathrm{\le}c\mathrm{\}}$ is uniformly integrable for each $c\mathrm{\ge}\mathrm{0}$.

Title | Martingale criterion (continuous time) |
---|---|

Canonical name | MartingaleCriterioncontinuousTime |

Date of creation | 2013-03-22 18:54:26 |

Last modified on | 2013-03-22 18:54:26 |

Owner | karstenb (16623) |

Last modified by | karstenb (16623) |

Numerical id | 4 |

Author | karstenb (16623) |

Entry type | Theorem |

Classification | msc 60G07 |

Classification | msc 60G48 |