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<p>will</p> <p><b>New page</b></p><div>A &#039;&#039;&#039;stochastic process&#039;&#039;&#039; is a collection of [[Random variable|random variables]] indexed by time or space, representing the evolution of a system that incorporates randomness. Unlike deterministic processes, where the future is fixed by the present, a stochastic process admits multiple possible futures, each with an associated probability. The classic examples are the random walk, where a particle moves in steps whose directions are randomly chosen, and [[Brownian motion]], where a particle is buffeted by countless invisible collisions.<br /> <br /> Stochastic processes are the mathematical language of systems too complex to model deterministically: financial markets, neural firing patterns, genetic mutations, weather systems. They allow us to ask not what</div>

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