Define the stochastic process where . Find

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Expert Solution

A stochastic process is a family of random variables {Xθ}, where the parameter θ is drawn from an index set Θ. For example, let's say the index set is “time”. For a continuous process, the random variables are denoted by {Xt}, and for a discrete process they are denoted by {Xn}.

Some uses of stochastic process:

Poisson processes: for dealing with waiting times and queues.
Random Walk and Brownian motion processes: used in algorithmic trading.
Markov decision processes: commonly used in Computational Biology and Reinforcement Learning.
Gaussian Processes: used in regression and optimisation problems (eg. Hyper-Parameters tuning and Automated Machine Learning).
Auto-Regressive and Moving average processes: employed in time-series analysis (eg. ARIMA models).

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