Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Weak uniqueness and density estimates for sdes with coefficients depending on some path-functionals

Abstract : In this paper, we develop a general methodology to prove weak uniqueness for stochastic differential equations with coefficients depending on some path-functionals of the process. As an extension of the technique developed by Bass & Perkins [BP09] in the standard diffusion case, the proposed methodology allows one to deal with processes whose probability laws are singular with respect to the Lebesgue measure. To illustrate our methodology, we prove weak existence and uniqueness in two examples : a diffusion process with coefficients depending on its running symmetric local time and a diffusion process with coefficients depending on its running maximum. In each example, we also prove the existence of the associated transition density and establish some Gaussian upper-estimates.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [6 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01552492
Contributor : Noufel Frikha <>
Submitted on : Monday, July 3, 2017 - 8:57:36 AM
Last modification on : Friday, March 27, 2020 - 4:01:49 AM
Document(s) archivé(s) le : Thursday, December 14, 2017 - 6:11:18 PM

Files

weak_existence_sde_Final.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01552492, version 1
  • ARXIV : 1707.01295

Citation

Noufel Frikha, Libo Li. Weak uniqueness and density estimates for sdes with coefficients depending on some path-functionals. 2017. ⟨hal-01552492⟩

Share

Metrics

Record views

230

Files downloads

111