Jabarkan Implications of the definition dari Prosés stokastik dalam bahasa sunda

Of course, the mathematical definition of a function includes the case "a function from {1,...,n} to R is a vector in Rn", so multivariate random variables are a special case of stochastic processes.

For our first infinite example, take the domain to be N, the natural numbers, and our range to be R, the real numbers. Then, a function f : N → R is a sequence of réal numbers, and a stochastic process with domain N and range R is a random sequence. The following questions arise:

How is a random sequence specified?

How do we find the answers to typical questions about sequences, such as

what is the probability distribution of the value of f(i)?

what is the probability that f is bounded?

what is the probability that f is monotonic?

what is the probability that f(i) has a limit as i→∞?

if we construct a series from f(i), what is the probability that the series converges? What is the probability distribution of the sum?

Another important class of examples is when the domain is not a discrete space such as the natural numbers, but a continuous space such as the unit interval [0,1], the positive réal numbers [0,∞) or the entire real line, R. In this case, we have a different set of questions that we might want to answer:

How is a random function specified?

How do we find the answers to typical questions about functions, such as

what is the probability distribution of the value of f(x) ?

what is the probability that f is bounded/integrable/continuous/differentiable...?

what is the probability that f(x) has a limit as x→∞ ?

what is the probability distribution of the integral ?

There is an effective way to answer all of these questions, but it is rather technical (see Constructing Stochastic Processes below).