Stochastic Process

Stochastic Process is a mathematical model that describes the evolution of a system over time, where the evolution of the system is influenced by random or unpredictable events. Stochastic processes are used in a wide range of fields, including physics, engineering, finance, economics, and biology.
At its core, a stochastic process is simply a collection of random variables that are indexed by time or some other parameter. The random variables in a stochastic process represent the state of the system at different points in time. The evolution of the process over time is determined by the probabilities of different outcomes at each time step.
There are many different types of stochastic processes, each with its own characteristics and applications. Some common examples include:
# Markov processes: These are stochastic processes in which the probability of the next state depends only on the current state, and not on any previous states.
# Brownian motion: This is a type of stochastic process that describes the random motion of particles in a fluid.
# Poisson processes: These are stochastic processes that model the occurrence of random events over time, such as the arrival of customers at a store or the decay of radioactive atoms.
# Random walks: These are stochastic processes in which a particle moves randomly in one or more dimensions, and the probability of its next move depends only on its current position.
Stochastic processes are used in many different areas of research and industry, such as predicting stock prices, analyzing weather patterns, and modeling the spread of infectious diseases. They are a powerful tool for understanding and predicting the behavior of complex systems in the presence of uncertainty and randomness.
Category:Mathematics
Category:Time Machine