# Stability Estimates for Finite-Dimensional Distributions of Time-Inhomogeneous Markov Chains

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Notation and Main Assumptions

## 3. Coupling of Two Independent Time-Inhomogeneous Markov Chains with Different Transition Probabilities

## 4. Auxiliary Lemmas

**Lemma**

**1.**

**Proof.**

**Lemma**

**2.**

**Proof.**

**Lemma**

**3.**

**Proof.**

**Lemma**

**4.**

**Proof.**

**Lemma**

**5.**

**Proof.**

## 5. Main Result

**Theorem**

**1.**

**Proof.**

## 6. The Case When Uniform Proximity Condition Is Violated

**Lemma**

**6.**

**Proof.**

**Lemma**

**7.**

**Lemma**

**8.**

**Theorem**

**2.**

**Proof.**

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**MDPI and ACS Style**

Golomoziy, V.; Mishura, Y.
Stability Estimates for Finite-Dimensional Distributions of Time-Inhomogeneous Markov Chains. *Mathematics* **2020**, *8*, 174.
https://doi.org/10.3390/math8020174

**AMA Style**

Golomoziy V, Mishura Y.
Stability Estimates for Finite-Dimensional Distributions of Time-Inhomogeneous Markov Chains. *Mathematics*. 2020; 8(2):174.
https://doi.org/10.3390/math8020174

**Chicago/Turabian Style**

Golomoziy, Vitaliy, and Yuliya Mishura.
2020. "Stability Estimates for Finite-Dimensional Distributions of Time-Inhomogeneous Markov Chains" *Mathematics* 8, no. 2: 174.
https://doi.org/10.3390/math8020174