Understanding a statement about Brownian motion processes Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Running maximum for Geometric Brownian MotionThe Brownian motion process in Sheldon M. RossAbsolute continuity and sample paths of Brownian motionDetails about Brownian motionTransience of Brownian MotionSimple question on interpreting Geometric Brownian Motion SDECrossing of Brownian Motion Sample PathsBrownian motion and conditional expectationIntroductory Brownian motion questionsIf $X(t)$ is a Brownian motion, show that $-X(t)$ is also a Brownian motion
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Understanding a statement about Brownian motion processes
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Running maximum for Geometric Brownian MotionThe Brownian motion process in Sheldon M. RossAbsolute continuity and sample paths of Brownian motionDetails about Brownian motionTransience of Brownian MotionSimple question on interpreting Geometric Brownian Motion SDECrossing of Brownian Motion Sample PathsBrownian motion and conditional expectationIntroductory Brownian motion questionsIf $X(t)$ is a Brownian motion, show that $-X(t)$ is also a Brownian motion
$begingroup$
A book I'm reading says, "an important result about Brownian motion is that, conditional on the value of the process at time $t$, the joint distribution of the process values up to time $t$ does not depend on the value of the drift parameter."
I've read this statement a few times, but it still doesn't make sense to me. I was wondering if someone could please clarify, or provide an example. I do not understand what they are saying. I know that for a Brownian motion $X(t)$, the random variable $X(t + y) - X(y)$ is independent of the process up to time $y$, but it appears that this statement is saying something different.
I do not want to just skip over this as the book says it's an "important result."
Thanks
brownian-motion
$endgroup$
add a comment |
$begingroup$
A book I'm reading says, "an important result about Brownian motion is that, conditional on the value of the process at time $t$, the joint distribution of the process values up to time $t$ does not depend on the value of the drift parameter."
I've read this statement a few times, but it still doesn't make sense to me. I was wondering if someone could please clarify, or provide an example. I do not understand what they are saying. I know that for a Brownian motion $X(t)$, the random variable $X(t + y) - X(y)$ is independent of the process up to time $y$, but it appears that this statement is saying something different.
I do not want to just skip over this as the book says it's an "important result."
Thanks
brownian-motion
$endgroup$
add a comment |
$begingroup$
A book I'm reading says, "an important result about Brownian motion is that, conditional on the value of the process at time $t$, the joint distribution of the process values up to time $t$ does not depend on the value of the drift parameter."
I've read this statement a few times, but it still doesn't make sense to me. I was wondering if someone could please clarify, or provide an example. I do not understand what they are saying. I know that for a Brownian motion $X(t)$, the random variable $X(t + y) - X(y)$ is independent of the process up to time $y$, but it appears that this statement is saying something different.
I do not want to just skip over this as the book says it's an "important result."
Thanks
brownian-motion
$endgroup$
A book I'm reading says, "an important result about Brownian motion is that, conditional on the value of the process at time $t$, the joint distribution of the process values up to time $t$ does not depend on the value of the drift parameter."
I've read this statement a few times, but it still doesn't make sense to me. I was wondering if someone could please clarify, or provide an example. I do not understand what they are saying. I know that for a Brownian motion $X(t)$, the random variable $X(t + y) - X(y)$ is independent of the process up to time $y$, but it appears that this statement is saying something different.
I do not want to just skip over this as the book says it's an "important result."
Thanks
brownian-motion
brownian-motion
asked Mar 27 at 3:55
user651921
add a comment |
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