On some fractional stochastic delay differential equations

✍ Scribed by Mahmoud M. El-Borai; Khairia El-Said El-Nadi; Hoda A. Fouad

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 427 KB
• Volume: 59
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/j.camwa.2009.05.004

✦ Synopsis

a b s t r a c t

We consider the Cauchy problem for an abstract stochastic delay differential equation driven by fractional Brownian motion with the Hurst parameter H > 1 2 . We prove the existence and uniqueness for this problem, when the coefficients have enough regularity, the diffusion coefficient is bounded away from zero and the coefficients are smooth functions with bounded derivatives of any order. We prove the theorem by using the convergence of the Picard-Lindelö f iterations in L 2 (Ω) to a solution of this problem which admits a smooth density with respect to Lebesgue's measure on R.