Increasing process
Encyclopedia
An increasing process is a stochastic process
where the random variable
s
which make up the process are increasing almost surely
and adapted
:
A continuous increasing process is such a process where the set
is continuous.
Stochastic process
In probability theory, a stochastic process , or sometimes random process, is the counterpart to a deterministic process...
where the random variable
Random variable
In probability and statistics, a random variable or stochastic variable is, roughly speaking, a variable whose value results from a measurement on some type of random process. Formally, it is a function from a probability space, typically to the real numbers, which is measurable functionmeasurable...
s
which make up the process are increasing almost surelyAlmost surely
In probability theory, one says that an event happens almost surely if it happens with probability one. The concept is analogous to the concept of "almost everywhere" in measure theory...
and adapted
Adapted process
In the study of stochastic processes, an adapted process is one that cannot "see into the future". An informal interpretation is that X is adapted if and only if, for every realisation and every n, Xn is known at time n...
:
A continuous increasing process is such a process where the set
is continuous.