Show that τ is a stopping time with respect to FX











up vote
1
down vote

favorite












https://i.stack.imgur.com/gvLDp.png



Given the probability space in the attached image I would like to Show that τ is a stopping time with respect to FX.



I have calculated the FX to be:



F0X=σ({X0})=(ØΩ)



F1X= σ({X0,X1)}= σ({a,b},{c,d})



F2X= σ(X0,X1,X2})= σ({a},{b},{c},{d})=2Ω



and I know from here my next step would be to calculate τ of each event. This is where I come unstuck as it appears that τ is actually 0,0,0,0 because at Time 0 the value is already above the stopping time of 10 therefore we never reach event 1 or 2. But if τ = 0 my understanding is it does not fit the criteria to be a stopping time. Excuse the beginner level question but can anyone help me work through this problem?



Many thanks






probability stopping-times







share|cite|improve this question


















  • 2




    Please use MathJax in future, @Sam.U
    – Shaun
    Nov 18 at 1:54










  • Why do you think that $tau=0$ is not a stopping time?
    – saz
    Nov 18 at 6:29















up vote
1
down vote

favorite












https://i.stack.imgur.com/gvLDp.png



Given the probability space in the attached image I would like to Show that τ is a stopping time with respect to FX.



I have calculated the FX to be:



F0X=σ({X0})=(ØΩ)



F1X= σ({X0,X1)}= σ({a,b},{c,d})



F2X= σ(X0,X1,X2})= σ({a},{b},{c},{d})=2Ω



and I know from here my next step would be to calculate τ of each event. This is where I come unstuck as it appears that τ is actually 0,0,0,0 because at Time 0 the value is already above the stopping time of 10 therefore we never reach event 1 or 2. But if τ = 0 my understanding is it does not fit the criteria to be a stopping time. Excuse the beginner level question but can anyone help me work through this problem?



Many thanks






probability stopping-times







share|cite|improve this question


















  • 2




    Please use MathJax in future, @Sam.U
    – Shaun
    Nov 18 at 1:54










  • Why do you think that $tau=0$ is not a stopping time?
    – saz
    Nov 18 at 6:29













up vote
1
down vote

favorite









up vote
1
down vote

favorite











https://i.stack.imgur.com/gvLDp.png



Given the probability space in the attached image I would like to Show that τ is a stopping time with respect to FX.



I have calculated the FX to be:



F0X=σ({X0})=(ØΩ)



F1X= σ({X0,X1)}= σ({a,b},{c,d})



F2X= σ(X0,X1,X2})= σ({a},{b},{c},{d})=2Ω



and I know from here my next step would be to calculate τ of each event. This is where I come unstuck as it appears that τ is actually 0,0,0,0 because at Time 0 the value is already above the stopping time of 10 therefore we never reach event 1 or 2. But if τ = 0 my understanding is it does not fit the criteria to be a stopping time. Excuse the beginner level question but can anyone help me work through this problem?



Many thanks






probability stopping-times







share|cite|improve this question













https://i.stack.imgur.com/gvLDp.png



Given the probability space in the attached image I would like to Show that τ is a stopping time with respect to FX.



I have calculated the FX to be:



F0X=σ({X0})=(ØΩ)



F1X= σ({X0,X1)}= σ({a,b},{c,d})



F2X= σ(X0,X1,X2})= σ({a},{b},{c},{d})=2Ω



and I know from here my next step would be to calculate τ of each event. This is where I come unstuck as it appears that τ is actually 0,0,0,0 because at Time 0 the value is already above the stopping time of 10 therefore we never reach event 1 or 2. But if τ = 0 my understanding is it does not fit the criteria to be a stopping time. Excuse the beginner level question but can anyone help me work through this problem?



Many thanks






probability stopping-times




probability stopping-times






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Nov 18 at 1:51









Sam.U

112




112








  • 2




    Please use MathJax in future, @Sam.U
    – Shaun
    Nov 18 at 1:54










  • Why do you think that $tau=0$ is not a stopping time?
    – saz
    Nov 18 at 6:29














  • 2




    Please use MathJax in future, @Sam.U
    – Shaun
    Nov 18 at 1:54










  • Why do you think that $tau=0$ is not a stopping time?
    – saz
    Nov 18 at 6:29








2




2




Please use MathJax in future, @Sam.U
– Shaun
Nov 18 at 1:54




Please use MathJax in future, @Sam.U
– Shaun
Nov 18 at 1:54












Why do you think that $tau=0$ is not a stopping time?
– saz
Nov 18 at 6:29




Why do you think that $tau=0$ is not a stopping time?
– saz
Nov 18 at 6:29















active

oldest

votes











Your Answer





StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");

StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});

function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});


}
});














draft saved

draft discarded


















StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3003056%2fshow-that-%25cf%2584-is-a-stopping-time-with-respect-to-fx%23new-answer', 'question_page');
}
);

Post as a guest















Required, but never shown






























active

oldest

votes













active

oldest

votes









active

oldest

votes






active

oldest

votes
















draft saved

draft discarded




















































Thanks for contributing an answer to Mathematics Stack Exchange!


  • Please be sure to answer the question. Provide details and share your research!

But avoid …



  • Asking for help, clarification, or responding to other answers.

  • Making statements based on opinion; back them up with references or personal experience.


Use MathJax to format equations. MathJax reference.


To learn more, see our tips on writing great answers.





Some of your past answers have not been well-received, and you're in danger of being blocked from answering.


Please pay close attention to the following guidance:


  • Please be sure to answer the question. Provide details and share your research!

But avoid …



  • Asking for help, clarification, or responding to other answers.

  • Making statements based on opinion; back them up with references or personal experience.


To learn more, see our tips on writing great answers.




draft saved


draft discarded














StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3003056%2fshow-that-%25cf%2584-is-a-stopping-time-with-respect-to-fx%23new-answer', 'question_page');
}
);

Post as a guest















Required, but never shown





















































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown

































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown







-

Popular posts from this blog

AnyDesk - Fatal Program Failure

Image
up vote 0 down vote favorite Good day all. I have a window that pops up saying Fatal Program Failure (AnyDesk). This is what I have done so far: Uninstalled AnyDesk and reinstalled it. ( The window still appeared ) I disabled AnyDesk start up in Msconfig and the window seems to have disapeared. Lastly I made sure that AnyDesk worked by remoting into it, and it worked. Today the same window appeared. How do I get rid of this window? remote-desktop share | improve this question edited 10 hours ago Tomasz Jakub Rup 552 3 13 ...
Read more

How to calibrate 16:9 built-in touch-screen to a 4:3 resolution?

Image
up vote 0 down vote favorite I need help with an issue we're facing in a project where we are moving from a Windows-based POS environment to one running on CentOS7. The problem consists of a number of factors, please find the details below: The supplier of our POS application will only deliver an application that is hard-coded to run in a 1024:768 4:3 format. The hardware we are using is a POS unit from HP that has a built-in 16:9 touch-screen. The employees using this solution is not supposed to see nor have access to anything but the POS application. Our sales organization demands that touch is an available feature when going live with the new POS environment. Going further into this, allow me to explain what we have encountered on the way trying to achieve the goal of having a touch-screen: We've simply change...
Read more

QoS: MAC-Priority for clients behind a repeater

Image
1 1 I've setup a wireless network using a Linksys-Router (DD-WRT) as an AP and a TP-Link repeater for range extension. To manage bandwith for specific users, I've setup QoS-Rules on the AP (DD-WRT) using MAC-Priority: However the AP shows only the Repeater's MAC and the MACs of users inside the AP-Range. The MAC addresses of users behind the Repeater are not listed : The purple MAC is not listed in the AP-Clientlist. Its related to a device connected via the TP-Link repeater. Q: How can I setup MAC-Priority for repeater-clients? Do I simply add the purple MAC in AP-MAC priority list although it's not listed as a client? I want to setup specific priority instead of giving one priority for all clients behind the repeater by adding the repeater's MAC in the MAC priority list in the AP as ...
Read more