Local limit theorem for a perturbed sample paths of induced order statistics
- Авторлар: Bitter I.I.1
-
Мекемелер:
- Laboratory of Stochastic Analysis and its Applications, HSE University
- Шығарылым: № 113 (2025)
- Беттер: 6-20
- Бөлім: Systems analysis
- URL: https://ogarev-online.ru/1819-2440/article/view/289704
- ID: 289704
Дәйексөз келтіру
Толық мәтін
Аннотация
In this paper we derive a local limit theorem for a perturbed sample paths of normalized sums of induced order statistics obtained from a sequence of independent identically distributed random vectors under weak regularity conditions on the coefficients. The situation under consideration is a typical example of the problem of estimating the rate of convergence of discrete-time Markov processes to diffusions, when the corresponding trends and diffusion coefficients of the Markov chain and the diffusion limit coincide only asymptotically. Under the conditions described above, the classical result of Konakov and Mammen (2000) on the rate of weak convergence of triangular arrays of discrete Markov processes to a diffusion process with coefficients that coincide with the coefficients of the chains turns out to be inapplicable. Our approach is based on the study of the uniform distance between the transition densities of the underlying inhomogeneous Markov chain and the limiting gaussian diffusion process. In particular, the convergence rate estimate derived from the well-known classical limit theorem and the parametrix-type stability bounds.
Негізгі сөздер
Авторлар туралы
Ilya Bitter
Laboratory of Stochastic Analysis and its Applications, HSE University
Email: ilya.bitter@yandex.ru
Moscow
Әдебиет тізімі
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