Stochastic

Stochastic refers to a mathematical concept that is defined by a random probability distribution or pattern that can be statistically analyzed. It is typically used in the field of mathematics and physics to represent systems or processes that have a degree of randomness or unpredictability.

Definition

The term "stochastic" comes from the Greek word "stokhazesthai" which means "to aim at a target". In the context of mathematics and physics, it is used to describe systems or processes that have a degree of randomness or unpredictability. This randomness can be due to the inherent unpredictability of the system or process, or it can be due to the lack of complete information about the system or process.

Applications

Stochastic processes are used in a variety of fields, including physics, chemistry, engineering, finance, and medicine. They are used to model systems or processes that exhibit randomness or unpredictability. Some examples of stochastic processes include the movement of particles in a fluid, the behavior of stock prices, and the spread of diseases in a population.

Stochastic Processes

A stochastic process is a collection of random variables representing the evolution of some system of random values over time. This could be the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule. They are used to model the behavior of systems that change over time in a random way.

Stochastic Calculus

Stochastic calculus is a branch of mathematics that operates on stochastic processes. It allows a consistent theory of integration to be defined for integrals of stochastic processes with respect to stochastic processes. It is used to model systems that behave randomly. The best-known stochastic process to which stochastic calculus is applied is the Wiener process, which is used for modeling Brownian motion as described by Louis Bachelier in 1900 and by Albert Einstein in 1905 and other physical diffusion processes in space of particles subject to random forces.

See Also

• Probability theory
• Randomness
• Statistics
• Markov process
• Brownian motion

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