But what the
Stochastic process showed me was that it doesn't matter what our past is; what matters is our present, because how we live our present can tell us about our future.
An adapted continuous
stochastic process [U.sub.t] (resp., [L.sub.t]) is an upper (resp., lower) solution of SDE (1) if the inequalities
The second and the third statements are a direct consequence of the definitions of the spaces [M.sup.[gamma].sub.p] and [[??].sup.[gamma].sub.p] and the inequality [mathematical expression not reproducible], which holds for any measurable
stochastic process y(t).
In probability theory and related fields, a Markov process (named after the Russian mathematician Andrey Markov), is a
stochastic process that satisfies the "memorylessness" property, meaning that one can make predictions for the future of the process based solely on its present state, independently from its history.
We also recall the notions of fuzzy random variable and fuzzy
stochastic process. In Section 3, we discuss the RFDEs with impulses.
In 1965, Priestley proposed evolutionary
stochastic process [5] theory in which a nonstationary process is converted to an integral of a stationary process and a deterministic modulation function, and then, the time-varying spectrum density of the nonstationary process is obtained from the spectrum density of the stationary process, and a method of describing the characteristics of the spectrum of a nonstationary process and a model of nonstationary ground motion is created.
A
stochastic process x : I x J x [OMEGA] [right arrow] [R.sup.d] is said to be {[F.sub.s,t]}-adapted, if [x.sub.s,t] : [OMEGA] [right arrow] [R.sup.d] is an [F.sub.s,t]-measurable random vector for every fixed (s, t) [member of] I x J.
is called a generalized
stochastic process on [R.sup.d].
A
Stochastic process is a system expressing a phenomenon or experiment developed in some time with random variables.
Pindyck (1999 ) argues that the ADF test is not sufficient to determine the choice of the
stochastic process, and recommends using another approach that reflects the series behavior of the feature before price shocks, in that temporary impacts in the series show a behavior of mean reversion.