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Các trường Poisson phân đoạn và các martingale
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.Tài liệu tham khảo
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