Markov Processes
Markov Processes are a powerful tool for modelling and analysing systems that evolve over time. Markov Processes are stochastic processes, which means that their behaviour is determined by randomness rather than pre-determined logic. This makes them especially useful for predicting the behaviour of systems over time where certain elements are uncertain.
At its core, a Markov Process is a mathematical description of how a system evolves over time. To define a Markov Process, we first need to define a set of possible states that the system can exist in, as well as the transitions between these states. We can then assign probabilities to each of these transitions, describing the likelihood of moving from one state to another.
Once these probabilities have been assigned, we can then calculate the probability of being in any given state at any given time in the future. This property, known as the Markov property, is what makes Markov Processes so powerful. From these probabilities, we can construct a model of the system, which allows us to make predictions about its future behaviour.
Perhaps the most common application for Markov Processes is in modelling and predicting the behaviour of things like financial markets, epidemics or the weather. In each of these cases, the system under consideration has a set of possible states that it can exist in and transitions between these states. By assigning probabilities to these transitions, we can model the system over time and make predictions about its future.
In addition to these applications, Markov Processes are also used to model and predict the behaviour of many biological systems, such as the spread of viruses or the evolution of species. Again, by assigning probabilities to the transitions between states, we can create a model of the system and make predictions about its future behaviour.
Finally, Markov Processes are also used in artificial intelligence and machine learning. By training models on a Markov Process, we can use them to make predictions about the behaviour of a system. For example, Markov Processes are used to drive autonomous vehicles such as self-driving cars. By training a model on a Markov Process representing different states that the car can be in, and different transitions between these states, the car can make intelligent decisions about how to navigate its environment.
Markov Processes are a powerful tool for modelling and predicting the behaviour of systems over time. By assigning probabilities to the transitions between states, we can create a model of the system and make predictions about its future. This has allowed Markov Processes to be successfully applied to a variety of different domains, including finance, biology, and artificial intelligence.
