Giải tích Malliavin cho các phương trình trễ phân thức

Springer Science and Business Media LLC - Tập 25 - Trang 854-889 - 2011
Jorge A. León1, Samy Tindel2
1Depto. de Control Automático, CINVESTAV-IPN, Mexico, Mexico
2Institut Élie Cartan Nancy, Vandoeuvre-lès-Nancy Cedex, France

Tóm tắt

Trong bài báo này, chúng tôi nghiên cứu sự tồn tại của một nghiệm duy nhất cho một lớp tổng quát các phương trình vi phân trễ Young, được điều khiển bởi một hàm liên tục Hölder với tham số lớn hơn 1/2 thông qua thiết lập tích phân Young. Sau đó, một số ước lượng cho nghiệm được thu được, cho phép chứng minh rằng nghiệm của phương trình vi phân trễ được điều khiển bởi chuyển động Brown phân thức (fBm) với tham số Hurst H > 1/2 có mật độ C ∞. Để đạt được mục đích này, chúng tôi sử dụng giải tích Malliavin dựa trên tính khả vi Fréchet theo các phương hướng của không gian Hilbert hạt nhân tái tạo liên quan đến fBm.

Từ khóa

#phương trình vi phân trễ #tích phân Young #hàm liên tục Hölder #chuyển động Brown phân thức #mật độ C∞ #giải tích Malliavin

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854-889

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