# Markov Analysis.

Markov analysis is a tool used by financial analysts to predict future prices of assets based on past price movements. The technique is named after Andrey Markov, a Russian mathematician who developed the theory behind it.

Markov analysis is based on the assumption that future price movements of an asset will be based on its past price movements. The technique involves constructing a model of an asset's price movements using a series of past prices. This model is then used to predict future prices of the asset.

Markov analysis is a powerful tool that can be used to predict future prices of assets with a high degree of accuracy. However, the technique is complex and requires a good understanding of mathematics and statistics.

What are the basic properties of the Markov model? The Markov model is a mathematical model used to predict the probability of future states, based on the assumption that the future state is only dependent on the current state. This means that the model only considers the present, without taking into account any past information.

The Markov model is named after Andrey Markov, who was the first to develop the model. What are the properties of Markov chain? A Markov chain is a stochastic model used to describe a sequence of possible events in which the probability of each event depends only on the state of the system at the previous event. In other words, the future state of the system is completely determined by its current state.

The properties of a Markov chain can be summarized as follows:

1. The system is in a definite state at any given time.

2. The system can only transition to other states that are adjacent to its current state.

3. The probability of transitioning to any particular state is constant over time.

4. The system is memoryless, meaning that the probability of transitioning to any particular state is independent of the previous history of the system. What is Markov process and give an example? A Markov process is a type of stochastic process where the future behaviour of the process is completely determined by its present state, without regard for its past history.

A simple example of a Markov process is a random walk. If we know the current position of the walker, then their next step is completely determined by a coin flip. Their future position is not affected by their past position. What are the characteristics of Markov process? A Markov process is a stochastic process with the Markov property. This property states that the future evolution of the process is completely determined by its present state, without reference to its past history.

A Markov process is therefore said to be "memoryless": the future evolution of the process is not affected by its past history. This makes the Markov process a powerful tool for modeling stochastic processes, as it is often much easier to determine the present state of a system than its past history.

The Markov property is named after Andrey Markov, who was the first to formalize the concept.

#### How HMM is used in NLP?

HMM is a tool that can be used for various tasks in NLP, such as part-of-speech tagging, parsing, and machine translation.

One of the most popular applications of HMM is part-of-speech tagging. In this task, the goal is to assign a part-of-speech tag (e.g., noun, verb, etc.) to each word in a sentence.

HMM can be used for this task by modeling the sentence as a sequence of Observed Words (OWs) and Hidden States (HSs). The HSs represent the part-of-speech tags of the words in the sentence, while the OWs are the words themselves.

The HMM model is then trained on a large corpus of sentences, using the Baum-Welch algorithm.

Once the model is trained, it can be used to tag new sentences. The Viterbi algorithm is used to find the most likely sequence of HSs for a given sentence.

HMM can also be used for parsing, which is the task of extracting the grammatical structure of a sentence.

In this task, the HMM model is again used to model the sentence as a sequence of OWs and HSs. But this time, the HSs represent the grammatical relations between the words in the sentence (e.g., subject, object, etc.).

The model is trained on a corpus of sentences, and then used to parse new sentences. The Viterbi algorithm is used to find the most likely sequence of HSs for a given sentence.

HMM can also be used for machine translation. In this task, the HMM model is used to model the source sentence as a sequence of OWs and HSs, and the target sentence as a sequence of OWs.

The HSs in the source sentence represent the meaning of the words, while the HSs in