Các trường Poisson phân đoạn và các martingale

Journal of Statistical Physics - Tập 170 - Trang 700-730 - 2018
Giacomo Aletti1, Nikolai Leonenko2, Ely Merzbach3
1ADAMSS Center, Università degli Studi di Milano, Milan, Italy
2Cardiff University, Cardiff, UK
3Bar-Ilan University, Ramat-Gan, Israel

Tóm tắt

Chúng tôi trình bày những đặc điểm mới của quá trình Poisson phân đoạn (FPP) và trường Poisson phân đoạn trên mặt phẳng. Một đặc điểm martingale cho các FPP được đưa ra. Chúng tôi mở rộng kết quả này cho các trường Poisson phân đoạn, thu được một số đặc điểm khác. Các phương trình vi phân phân đoạn được nghiên cứu. Chúng tôi xem xét một quá trình Poisson hỗn hợp-phân đoạn tổng quát hơn và chỉ ra rằng quá trình này là giải pháp ngẫu nhiên của một hệ thống các phương trình vi phân-thoái hóa phân đoạn. Cuối cùng, chúng tôi đưa ra một số mô phỏng của trường Poisson phân đoạn trên mặt phẳng.

Từ khóa

#Quá trình Poisson phân đoạn #trường Poisson phân đoạn #martingale #phương trình vi phân phân đoạn #mô phỏng.

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