Abstract second-order damped McKean-Vlasov stochastic evolution equations

Mahmudov N., McKibben M.

Stochastic Analysis and Applications, vol.24, no.2, pp.303-328, 2006 (SCI-Expanded, Scopus) identifier

  • Nəşrin Növü: Article / Article
  • Cild: 24 Say: 2
  • Nəşr tarixi: 2006
  • Doi nömrəsi: 10.1080/07362990500522247
  • jurnalın adı: Stochastic Analysis and Applications
  • Jurnalın baxıldığı indekslər: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Səhifə sayı: pp.303-328
  • Açar sözlər: Approximate and exact controllability, Cosine family, McKean-Vlasov equation, Stochastic evolution equation
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Yox

Qısa məlumat

We establish results concerning the global existence, uniqueness, approximate, and exact controllability of mild solutions for a class of abstract second-order stochastic evolution equations in a real separable Hilbert space in which we allow the nonlinearities at a given time t to depend not only on the state of the solution at time t , but also on the corresponding probability distribution at time t . First-order equations of McKean-Vlasov type were first analyzed in the finite dimensional setting when studying diffusion processes, and then subsequently extended to the Hilbert space setting. The current manuscript provides a formulation of such results for second-order problems. Examples illustrating the applicability of the general theory are also provided.