Stochastic Process

Stochastic Process

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A stochastic process is a mathematical concept used to represent systems or phenomena that evolve over time in a probabilistic manner. It is a sequence of random variables representing the evolution of a system of random values over time.

Each random variable in the sequence represents the state of the system at a particular time point. The randomness suggests that the future state of the process (i.e., the next value in the sequence) is not entirely predictable and is subject to chance, although it may be influenced by the current or past states.

Stochastic processes are used in a wide range of fields, including physics, chemistry, economics, finance, signal processing, and artificial intelligence. They are particularly useful in situations where the system being modeled is inherently random or unpredictable.

Examples of stochastic processes include:

Random Walk: This is a simple stochastic process where each step is determined by a random draw from a distribution. Stock market prices are often modeled as a type of random walk.

Markov Chains: These are stochastic processes where the probability of each next state depends only on the current state and not on the sequence of events that preceded it.

Poisson Process: This is a type of stochastic process where events occur continuously and independently at a constant average rate.

In machine learning and AI, stochastic processes are often used in reinforcement learning, Bayesian inference, and generative models, among other areas.

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