Метод параметрикса и его применение в теории вероятностей Кожина Анна Александровна

Короткий опис

Кожина, Анна Александровна.
Метод параметрикса и его применения в теории вероятностей = Parametrix Method and its Applications in Probability Theory : Parametrix Method and its Applications in Probability Theory : диссертация ... кандидата физико-математических наук : 01.00.00 / Anna Kozhina; [Место защиты: НИУ "Высшая школа экономики"]. - Москва, 2018. - 96 с.
Оглавление диссертациикандидат наук Кожина Анна Александровна
Contents
Glossary
1 Introduction
2 Parametrix technique
2.1 Review
2.2 Other developments in Parametrix
2.3 The parametrix method for diffusion processes
2.4 Markov Chains
3 Stability of diffusion transition densities
3.1 Stability results
3.1.1 Assumptions and Main Results
3.1.2 On Some Related Applications
3.1.3 Derivation of formal series expansion for densities
3.1.4 Stability of Parametrix Series
3.1.5 Stability for Markov Chains
4 Degenerate diffusions
4.1 Introduction
4.1.1 Hypoellipticity
4.1.2 Kolmogorov's example
4.1.3 Degeneracy and Hormander conditions
4.1.4 General models
4.1.5 Preliminary results from [KMM10]
4.2 Parametrix in the degenerate case
4.2.1 Assumptions
4.2.2 Parametrix expansion. Diffusion
4.3 Stability results
4.3.1 Stability for perturbed diffusions
4.4 Weak error
4.5 Global error
4.5.1 Proof of Theorem
4.6 Appendix