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Lecture

Markov Chains: State Classification

Description

This lecture covers the classification of states in discrete-time Markov chains. It discusses the concept of periodicity, irreducibility, and multiple of a period. The lecture also explores the conditions under which a state is periodic and the implications of periodicity on the chain.

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Related concepts (31)

Periodic table

The periodic table, also known as the periodic table of the elements, arranges the chemical elements into rows ("periods") and columns ("groups"). It is an organizing icon of chemistry and is widely used in physics and other sciences. It is a depiction of the periodic law, which says that when the elements are arranged in order of their atomic numbers an approximate recurrence of their properties is evident. The table is divided into four roughly rectangular areas called blocks.

Periodic trends

In chemistry, periodic trends are specific patterns that are present in the Periodic table that illustrate different aspects of certain elements when grouped by period and/or group. They were discovered by the Russian chemist Dmitri Mendeleev in the year 1863. Major periodic trends include atomic radius, ionization energy, electron affinity, electronegativity, valency and metallic character. These trends exist because of the similar electron configurations of the elements within their respective groups or periods; they reflect the periodic nature of the elements.

Edo period

The Edo period or Tokugawa period is the period between 1603 and 1867 in the history of Japan, when Japan was under the rule of the Tokugawa shogunate and the country's 300 regional daimyo. Emerging from the chaos of the Sengoku period, the Edo period was characterized by economic growth, strict social order, isolationist foreign policies, a stable population, perpetual peace, and popular enjoyment of arts and culture, colloquially referred to as Oedo.

Sengoku period

The Sengoku period is the period in Japanese history in which civil wars and social upheavals took place almost continuously in the 15th and 16th centuries. Though the Ōnin War (1467) is generally chosen as the Sengoku period's start date, there are many competing historiographies for its end date, ranging from 1568, the date of Oda Nobunaga's march on Kyoto, to the suppression of the Shimabara Rebellion in 1638, deep into what is traditionally considered the Edo period.

Markov chain

A Markov chain or Markov process is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happens next depends only on the state of affairs now." A countably infinite sequence, in which the chain moves state at discrete time steps, gives a discrete-time Markov chain (DTMC). A continuous-time process is called a continuous-time Markov chain (CTMC).

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