Research output: Contribution to journal › Article

A Lokka, B Oksendal, F Proske

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

Pages (from-to) | 1506 - 1528 |

Number of pages | 23 |

Journal | The Annals of Applied Probability |

Volume | 14 |

Issue number | 3 |

DOIs | |

Published | Aug 2004 |

In this paper we develop a white noise framework for the study of stochastic partial differential equations driven by a d-parameter (pure jump) Levy white noise. As an example we use this theory to solve the stochastic Poisson equation with respect to Levy white noise for any dimension d. The solution is a stochastic distribution process given explicitly. We also show that if d\leq 3, then this solution can be represented as a classical random field in L2(\mu ), where \mu is the probability law of the Levy process. The starting point of our theory is a chaos expansion in terms of generalized Charlier polynomials. Based on this expansion we define Kondratiev spaces and the Levy Hermite transform.

King's College London - Homepage

© 2020 King's College London | Strand | London WC2R 2LS | England | United Kingdom | Tel +44 (0)20 7836 5454