Weak convergence of random processes with immigration at random times
Abstrak
By a random process with immigration at random times we mean a shot noise process with a random response function (response process) in which shots occur at arbitrary random times. The so defined random processes generalize random processes with immigration at the epochs of a renewal process which were introduced in [Iksanov et al. (2017). Bernoulli, 23, 1233--1278] and bear a strong resemblance to a random characteristic in general branching processes and the counting process in a fixed generation of a branching random walk generated by a general point process. We provide sufficient conditions which ensure weak convergence of finite-dimensional distributions of these processes to certain Gaussian processes. Our main result is specialised to several particular instances of random times and response processes.
Topik & Kata Kunci
Penulis (2)
Congzao Dong
Alexander Iksanov
Akses Cepat
- Tahun Terbit
- 2019
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓