Existence and Uniqueness of Stationary Probability Vector for Stochastic Matrices using Farkas’ Lemma

نویسندگان

چکیده

The purpose of this note is to provide a simple proof existence stationary probability vectors (fixed points) for stochastic matrices using Farkas’ lemma. This result as well the uniqueness also holds certain subclass quasi-stochastic matrices.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

analysis of ruin probability for insurance companies using markov chain

در این پایان نامه نشان داده ایم که چگونه می توان مدل ریسک بیمه ای اسپیرر اندرسون را به کمک زنجیره های مارکوف تعریف کرد. سپس به کمک روش های آنالیز ماتریسی احتمال برشکستگی ، میزان مازاد در هنگام برشکستگی و میزان کسری بودجه در زمان وقوع برشکستگی را محاسبه کرده ایم. هدف ما در این پایان نامه بسیار محاسباتی و کاربردی تر از روش های است که در گذشته برای محاسبه این احتمال ارائه شده است. در ابتدا ما نشا...

15 صفحه اول

A Discrete Farkas Lemma

Given A ∈ Zm×n and b ∈ Zm, we consider the issue of existence of a nonnegative integral solution x ∈ Nn to the system of linear equations Ax = b. We provide a discrete and explicit analogue of the celebrated Farkas lemma for linear systems in Rn and prove that checking existence of integral solutions reduces to solving an explicit linear programming problem of fixed dimension, known in advance.

متن کامل

The Farkas Lemma Revisited

The Farkas Lemma is extended to simultaneous linear operator and polyhedral sublinear operator inequalities by Boolean valued analysis. Introduction The Farkas Lemma, also known as the Farkas–Minkowski Lemma, plays a key role in linear programming and the relevant areas of optimization (cp. [1]). Some rather simple proof of the lemma is given in [2]. Using the technique of Boolean valued analys...

متن کامل

On Existence and Uniqueness of Stationary Distributions for Stochastic Delay Differential Equations with Positivity Constraints∗

Deterministic dynamic models with delayed feedback and state constraints arise in a variety of applications in science and engineering. There is interest in understanding what effect noise has on the behavior of such models. Here we consider a multidimensional stochastic delay differential equation with normal reflection as a noisy analogue of a deterministic system with delayed feedback and po...

متن کامل

On Existence and Uniqueness of Stationary Distributions for Stochastic Delay Differential Equations with Non-Negativity Constraints∗

Deterministic dynamic models with delayed feedback and state constraints arise in a variety of applications in science and engineering. There is interest in understanding what effect noise has on the behavior of such models. Here we consider a multidimensional stochastic delay differential equation with normal reflection as a noisy analogue of a deterministic system with delayed feedback and no...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Asian Journal of Probability and Statistics

سال: 2022

ISSN: ['2582-0230']

DOI: https://doi.org/10.9734/ajpas/2022/v20i4442