Rate of Weak Convergence of Random Walk with a Generalized Reflecting Barrier

Başak Gever; Tahir Khanıyev

Makale detayları

Rate of Weak Convergence of Random Walk with a Generalized Reflecting Barrier

Yazarlar:

Başak Gever | Tahir Khanıyev

Yayıncı:

Gazi University

Ana Başlıklar:

Stochastic (Probability ) Process

Dergi:

Gazi University Journal of Science Vol.38 Issue 1, pp.474-490

Belge Tipi:

Makale

Yayın Tarihi:

1/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001341119

pISSN:

2147-1762

Anahtar kelimeler:

Özet:

 In this study, a random walk process with generalized reflecting barrier is considered and an inequality for rate of weak convergence of the stationary distribution of the process of interest is propounded. Though the rate of convergence is not thoroughly examined, the literature does provide a weak convergence theorem under certain conditions for the stationary distribution of the process under consideration. Nonetheless, one of the most crucial issues in probability theory is the convergence rate in limit theorems, as it affects the precision and effectiveness of using these theorems in practice. Therefore, for the rate of convergence for the examined process, comparatively simple inequality is represented. The obtained inequality demonstrates that the rate of convergence is correlated with the tail of the distribution of ladder heights of the random walk.

 In this study, a random walk process with generalized reflecting barrier is considered and an inequality for rate of weak convergence of the stationary distribution of the process of interest is propounded. Though the rate of convergence is not thoroughly examined, the literature does provide a weak convergence theorem under certain conditions for the stationary distribution of the process under consideration. Nonetheless, one of the most crucial issues in probability theory is the convergence rate in limit theorems, as it affects the precision and effectiveness of using these theorems in practice. Therefore, for the rate of convergence for the examined process, comparatively simple inequality is represented. The obtained inequality demonstrates that the rate of convergence is correlated with the tail of the distribution of ladder heights of the random walk.

 In this study, a random walk process with generalized reflecting barrier is considered and an inequality for rate of weak convergence of the stationary distribution of the process of interest is propounded. Though the rate of convergence is not thoroughly examined, the literature does provide a weak convergence theorem under certain conditions for the stationary distribution of the process under consideration. Nonetheless, one of the most crucial issues in probability theory is the convergence rate in limit theorems, as it affects the precision and effectiveness of using these theorems in practice. Therefore, for the rate of convergence for the examined process, comparatively simple inequality is represented. The obtained inequality demonstrates that the rate of convergence is correlated with the tail of the distribution of ladder heights of the random walk.

 In this study, a random walk process with generalized reflecting barrier is considered and an inequality for rate of weak convergence of the stationary distribution of the process of interest is propounded. Though the rate of convergence is not thoroughly examined, the literature does provide a weak convergence theorem under certain conditions for the stationary distribution of the process under consideration. Nonetheless, one of the most crucial issues in probability theory is the convergence rate in limit theorems, as it affects the precision and effectiveness of using these theorems in practice. Therefore, for the rate of convergence for the examined process, comparatively simple inequality is represented. The obtained inequality demonstrates that the rate of convergence is correlated with the tail of the distribution of ladder heights of the random walk.

Makale detayları

Rate of Weak Convergence of Random Walk with a Generalized Reflecting Barrier

Yazarlar:

Başak Gever | Tahir Khanıyev

Yayıncı:

Gazi University

Ana Başlıklar:

Stochastic (Probability ) Process

Dergi:

Gazi University Journal of Science Vol.38 Issue 1, pp.474-490

Belge Tipi:

Makale

Yayın Tarihi:

1/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001341119

pISSN:

2147-1762

Inequality for Asymptotic Rate

Weak Convergence

Random Walk

Reflecting Barrier

Sayı

Makale detayları

Rate of Weak Convergence of Random Walk with a Generalized Reflecting Barrier

Yazarlar: Başak Gever | Tahir Khanıyev

Yayıncı: Gazi University

Ana Başlıklar: Stochastic (Probability ) Process

Dergi: Gazi University Journal of Science Vol.38 Issue 1, pp.474-490

Belge Tipi: Makale

Yayın Tarihi: 1/2025

Belge Dili: İngilizce

Document ID (Org No.): 2001341119

pISSN: 2147-1762

Inequality for Asymptotic Rate

Weak Convergence

Random Walk

Reflecting Barrier

Sayı

Yazarlar:

Başak Gever | Tahir Khanıyev

Yayıncı:

Gazi University

Ana Başlıklar:

Stochastic (Probability ) Process

Dergi:

Gazi University Journal of Science Vol.38 Issue 1, pp.474-490

Belge Tipi:

Makale

Yayın Tarihi:

1/2025

Belge Dili:

İngilizce

Document ID (Org No.):

2001341119

pISSN:

2147-1762