Markov Processes Assignment Help
Markov process is a statistical method used to forecast or estimate values of variables whose predicted values are influenced by their current state, not by their prior activities. Ideally, Markov processes predict random variables based solely on the circumstances that currently surround the variables. This technique gets its name from Andrei Andreyevich Markov, a Russian mathematician who pioneered the study and analysis of stochastic processes. He first used these processes to predict the movement of gas molecules trapped in a container. Today, Markov processes are used to predict decisions and behaviors within different groups of people.
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Advantages And Disadvantages Of Markov Processes
The main benefit of Markov processes is simplicity. They are also more accurate than other data forecasting processes. Simple models developed with Markov processes are often better at making forecasts than more complex models.
Markov processes are not very effective in explaining the cause of a problem. Sure, it would help us come up with possible solutions to the problem but it will tell us very little about why the problem occurred. For example, in engineering, Markov processes will let us know the probability that a certain machine will break down but they won’t tell us why it breaks down. In finance, Markov processes face similar limitations. They will help us fix financial problems but not our lack of knowledge about the financial markets or how to avoid bad credits.
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Types Of Markov Processes
There are three different types of Markov processes:
- Discrete time Markov chain: In this Markov process, the system evolves through a discrete number of time steps. Therefore, a change to the system can only occur at one of the discrete time values. For example, consider a board game like the chutes and ladders, in which the pieces move around the board based on a dice roll. If you look at the board when the players are already halfway, you cannot tell how the players arrived at their current position, because the past history of the game doesn’t matter (previous history of the system). All what matters is the current position of the game (current state of the system) and the next dice roll (the probability aspect). This is a discrete time Markov process because the changes to the state of the system can only occur on someone’s turn. Learn more about discrete time Markov chains from our Markov processes homework helpers.
- Continuous time Markov chain: In a continuous time Markov process, the changes to the state of the system can occur at any time within a continuous interval. A good example would be the number of cars visiting a car wash in a given day. Arrivals are technically independent and cars can arrive at any time. If you know how many cars visited the car wash at say, 1100 hours, what happened before that won’t give you any useful information on estimating how many cars will have driven in by, say, 1300 hours. This is under the assumption that the arrival of the cars follows a continuous time Markov chain.
- Markov decision process: This is a Markov process that includes an agent that aids in making decisions that affect the evolvement of a system’s state over time. How this process works is that the agent selects actions and the system responds to these actions and presents new situations to the agent. An example of a Markov decision process would be an inventory for a supermarket. If you know how much bread you have by 0900 hours and trying to predict how much bread you will have by 1100 hours, the inventory levels before 0900 hours won’t tell you anything more than what you have already gathered about the levels at 0900 hours. The Markov decision process aspect comes to play if the manager decides to order more bread so that it arrives at certain times. Hence, the inventory level at 1100 hours will depend not only on customers arriving randomly and picking bread but also on the decision of the manager.
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Markov Processes Assignment Topics Covered By Our Experts
We provide different kinds of assistance for students who contact us for Markov processes assignment help. Our experts understand how important these papers are to students and so they work on each order diligently to meet the expectations of each client. Whether you need help with basic or advanced Markov processes topics, we can provide all kinds of help. We have provided Markov processes homework help on various topics to scholars of different educational levels. Some of the topics we have covered over the years include:
- Poisson processes
- Finite state Markov chains
- Classification of states
- Rates of convergence
- Random walks in 1, 2, and 3 dimensions
- Piecewise deterministic Markov analysis
- Calculation of N step
- Transition probabilities
- Birth and death processes
- Random walks on finite groups
- Feller processes
- Markov property
- Dirichlet form
- Spectral gap methods
- Convergence of equilibrium
- Ergodic chains
- Affine processes
- Stationary distribution
- Hitting probabilities
- Mean hitting times
- Diffusion processes
- Coupling methods
- Ehrenfest’s Urn model
- Strong Markov property
- Martingale problem
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