Locally integrable increasing processes with continuous compensators

D. Borzykh

?

Locally integrable increasing processes with continuous compensators

P. 43–47.

We prove that a joint distribution of a locally integrable increasing process X◦ and its compensator
A◦ at a terminal moment of time can be realized as a joint terminal distribution of another locally
integrable increasing process X* and its compensator A*, A* being continuous.

Language: English

Full text

Text on another site

Keywords: компенсатор compensator возрастающий процесс increasing process terminal joint distribution совместное терминальное распределение разложение Дуба--Мейера Doob–Meyer Decomposition

In book

Сборник материалов V-й Международной конференции по стохастическим методам: The 5th International Conference on Stochastic Methods (ICSM5). 23-27 November 2020, Russia, Moscow.

M.: RUDN, 2020.

Совместные распределения обобщенных интегрируемых возрастающих процессов и их обобщенных компенсаторов

Borzykh D., Теория вероятностей и ее применения 2024 Т. 69 № 1 С. 3–32

We consider the set $\Lambda$ of all edge joint distributions $\Law ([X_a, A_a], [X_b, A_b])$ at the moments $t =a$ and $t = b$ of integrable increasing processes $(X_t)_{t\in [a; b]}$ and their compensators $(A_t)_{t\in [a; b]}$, which start from an arbitrary integrable initial condition $[X_a, A_a]$. The convexity and closure of the set $\Lambda$ in ...

Added: April 13, 2022

On the denseness of the subset of discrete distributions in a certain set of two-dimensional distributions

Borzykh D., Gushchin A. A., Modern Stochastics: Theory and Applications 2022 Vol. 9 No. 3 P. 265–277

In the article [Theory of Probability & Its Applications 62(2) (2018), 216–235], a class W of terminal joint distributions of integrable increasing processes and their compensators was introduced. In this paper, it is shown that the discrete distributions lying in W form a dense subset in the set W for ψ-weak topology with a gauge function ψ of linear growth. ...

Added: March 25, 2022

On a property of joint terminal distributions of locally integrable increasing processes and their compensators

Borzykh D., Theory of Stochastic Processes 2018 Vol. 23 No. 39 (2) P. 7–20

In this paper we prove that a joint distribution of a locally integrable increasing process $X^{\circ}$ and its compensator $A^{\circ}$ at a terminal moment of time can be realized as a joint terminal distribution of another locally integrable increasing process $X^{\star}$ and its compensator $A^{\star}$, $A^{\star}$ being continuous. ...

Added: August 24, 2019

On possible relations between an increasing process and its compensator in the non-integrable case

A. A. Gushchin, Russian Mathematical Surveys 2018 Vol. 73 No. 5 P. 928–930

We prove that any distribution on the positive half-line with infinite expectation can be a distribution of the terminal value of an increasing process such that the difference between the terminal values of its compensator and the increasing process itself is 1. ...

Added: November 17, 2018

О возможных соотношениях между возрастающим процессом и его компенсатором в неинтегрируемом случае

А. А. Гущин, Успехи математических наук 2018 Т. 73 № 5 С. 189–190

Доказывается, что любое распределение на положительной полупрямой с бесконечным математическим ожиданием может быть распределением терминального значения возрастающего процесса, у которого разность терминальных значений компенсатора и самого возрастающего процесса равно 1. ...

Added: October 31, 2018