Stochastic Delay Equations with Hereditary Drift: Estimates of the Density

✍ Scribed by Marco Ferrante; Carles Rovira; Marta Sanz-Solé

• Book ID: 102593509
• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 335 KB
• Volume: 177
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.2000.3631

✦ Synopsis

We consider a family of stochastic differential equations with a drift depending on the past history and a delayed diffusion term perturbed by a small parameter =>0. We establish the asymptotic behaviour as = a 0 for the logarithm of the corresponding family of densities at a fixed time t>0. The proof needs large deviation estimates and Malliavin calculus.