A Markov Chain is a mathematical system that undergoes transitions from one state to another on a state space, where the probability of each state depends only on the state attained in the previous step. This 'memoryless' property, known as the Markov property, makes them particularly useful for modeling random processes in various fields such as economics, genetics, and computer science.

Markov Chains

A Markov Chain is a mathematical system that undergoes transitions from one state to another on a state space, with the probability of each state depending only on the previous state and not on the sequence of events that preceded it. This memoryless property is known as the Markov property, making Markov Chains particularly useful for modeling random processes in various fields such as finance, genetics, and computer science.

Markov Chain

mathematical system

transitions from one state to another

State space is a mathematical model used to describe a system by its states and the transitions between them, providing a framework for analyzing dynamic systems. It is a crucial concept in fields like control theory, artificial intelligence, and operations research, aiding in the understanding and prediction of system behavior over time.

state space

probability of each state

previous step

The memoryless property is a characteristic of certain stochastic processes where the future probability distribution of the process is independent of the past, given the present state. This property is most commonly associated with the exponential distribution in continuous time and the geometric distribution in discrete time, both of which describe the time until an event occurs in a Poisson process.

Memoryless Property

The Markov property is a fundamental characteristic of stochastic processes, where the future state of the process depends only on the present state and not on the sequence of events that preceded it. This memoryless property simplifies the analysis and modeling of complex systems in fields like physics, economics, and artificial intelligence.

Markov property

modeling random processes

Economics is the study of how individuals, businesses, and governments make choices on allocating resources to satisfy their wants and needs, and how these choices interact to shape markets and economies. It encompasses both microeconomic and macroeconomic perspectives, analyzing everything from individual consumer behavior to global economic trends.

economics

Genetics is the study of heredity and variation in living organisms, focusing on how traits are passed from parents to offspring through genes. It encompasses the molecular structure and function of genes, gene behavior in the context of a cell or organism, and patterns of inheritance across generations.

genetics

Computer science is the study of algorithmic processes, computational machines, and computation itself, which underpins the development of software and systems that drive modern technology. It encompasses a wide range of topics from theoretical foundations to practical applications, making it essential for innovation in various fields such as artificial intelligence, cybersecurity, and data science.

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