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modification of a stochastic process (Definition)

Let $ \lbrace X_t \rbrace_{t\geq 1}$, $ \lbrace Y_t\rbrace_{t\geq 1}$ be stochastic processes on $ (\Omega, \mathcal{F}, P)$. $ \lbrace X_t \rbrace_{t\geq 1}$ is a modification of $ \lbrace Y_t\rbrace_{t\geq 1}$ if

$\displaystyle P[\{\omega:X_t(\omega)=Y_t(\omega)\}]=1$
for all $ t \in [0, \infty).$

Bibliography

1
Bernt Øksendal. Stochastic Differential Equations, (An Introduction with Applications), 5th ed Springer 1998.



"modification of a stochastic process" is owned by georgiosl.
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See Also: distributions of a stochastic process

Also defines:  modification
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Cross-references: stochastic processes
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This is version 4 of modification of a stochastic process, born on 2006-08-12, modified 2006-08-15.
Object id is 8245, canonical name is ModificationOfAStochasticProcess.
Accessed 2168 times total.

Classification:
AMS MSC: 60G05 (Probability theory and stochastic processes :: Stochastic processes :: Foundations of stochastic processes)
 60G07 (Probability theory and stochastic processes :: Stochastic processes :: General theory of processes)
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