## Abstract

Let X be a Lei–Nualart process with Hurst index H∈(0,1), Z_{1} be an Hermite random variable. For any n ≥ 1, set (Formula Presented) The aim of the current paper is to derive, in the case when the Hurst index verifies H > 3/4, an upper bound for the total variation distance between the laws L(Z_{n}) and L(Z_{1}), where Z_{n} stands for the correct renormalization of V_{n} which converges in distribution towards Z_{1}. We derive also the asymptotic behavior of quadratic variations of process X in the critical case H=3/4, i.e. an upper bound for the total variation distance between the L(Z_{n}) and the Normal law.

Original language | English |
---|---|

Title of host publication | Stochastic Processes and Applications - SPAS2017 |

Editors | Sergei Silvestrov, Anatoliy Malyarenko, Milica Rančić |

Pages | 105-121 |

Number of pages | 17 |

DOIs | |

Publication status | Published - 1 Jan 2018 |

MoE publication type | A4 Article in a conference publication |

Event | International Conference on Stochastic Processes and Algebraic Structures – From Theory Towards Applications - Västerås and Stockholm, Sweden Duration: 4 Oct 2017 → 6 Oct 2017 |

### Conference

Conference | International Conference on Stochastic Processes and Algebraic Structures – From Theory Towards Applications |
---|---|

Abbreviated title | SPAS |

Country/Territory | Sweden |

City | Västerås and Stockholm |

Period | 04/10/2017 → 06/10/2017 |

## Keywords

- Berry–Esseen bounds
- Convergence in law
- Gaussian analysis
- Hermite random variable
- Malliavin calculus