# modification of a stochastic process

Let $\{X_{t}\}_{t\geq 0}$, $\{Y_{t}\}_{t\geq 0}$ be stochastic processes on $(\Omega,\mathcal{F},P)$. $\{X_{t}\}_{t\geq 0}$ is a modification of $\{Y_{t}\}_{t\geq 0}$ if

 $P[\{\omega:X_{t}(\omega)=Y_{t}(\omega)\}]=1$

for all $t\in[0,\infty).$

## References

• 1 Bernt Øksendal. , 5th ed Springer 1998.
Title modification of a stochastic process ModificationOfAStochasticProcess 2013-03-22 16:09:44 2013-03-22 16:09:44 georgiosl (7242) georgiosl (7242) 9 georgiosl (7242) Definition msc 60G07 msc 60G05 DistributionsOfAStochasticProcess modification