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#1 2012-06-22 15:50:39

lindah
Member
Registered: 2010-01-25
Posts: 121

Stopping times

Hi guys,

It has been a while!!

I have a quick question as follows:
Where X(t) is an Ito process and



Is

a stopping time?

May I ask what this notation

means?

I understand the maximum or minimum of two stopping times is a stopping time, but unsure how to explain this one.

Any hints would be greatly appreciated
Thank you
Linda

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#2 2012-06-22 19:50:07

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Stopping times

Hi lindah;

I am just getting into Martingales and stopping times and it has been rough going all the way. I do not know the answer to the question, I am reading some more right now. Looks like I could turn this pdf upside down and it would all be the same to me!


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#3 2012-06-23 08:57:30

lindah
Member
Registered: 2010-01-25
Posts: 121

Re: Stopping times

Hi bobbym;

I've been feeling that way about stochastic processes and calculus all semester!

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#4 2012-06-23 09:58:01

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Stopping times

Hi lindah;

Went through the stuff I have and only found one small video that the author was trying just a little to make understandable. Unfortunately he soon came to his senses and went back to his wallpaper math. He reasoned thusly: if I make someone who is reading this understand it then they will Yank me from Yale, Bust me from Berkeley, Move me from MIT, Heist me from Harvard, Drop me from Duke, Pull me from Princeton...

If I find something I will post it, sorry for not being able to help you.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#5 2012-06-23 10:06:43

lindah
Member
Registered: 2010-01-25
Posts: 121

Re: Stopping times

Hi bobbym;

That is okay! Thank you for looking.
It's such an abstract course, I keep running into walls of formulas, no practical examples etc

Btw I have just tried using math  site as you previously recommended. I was unaware of the site's etiquette and got a dressing down very early smile

Last edited by lindah (2012-06-23 10:35:01)

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#6 2012-06-23 10:12:39

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Stopping times

Hi;

I am sorry for that. Sorry for their highbrow attitude. They are precisely the people I am talking about. I have butted heads with some of them on other forums. On those forums they moderate and have made me as extinct as the dinosaur. Could you please give me the link?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#7 2012-06-23 10:18:54

lindah
Member
Registered: 2010-01-25
Posts: 121

Re: Stopping times

Hi bobbym;

It's more my fault for not reading the faq!

Link to annoying people removed by Administrator. No, not the real administrator, the other one.

Last edited by lindah (2012-06-23 10:21:03)

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#8 2012-06-23 10:24:47

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Stopping times

Hi;

The video gave a better example of some stopping times. As a dressing down goes that is moderate for them, probably because you are a girl.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#9 2012-06-23 10:36:22

lindah
Member
Registered: 2010-01-25
Posts: 121

Re: Stopping times

Hi;

Could you post a link to that video please?

Yes, bobbym that's why I like coming here!

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#10 2012-06-23 10:39:41

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Stopping times


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#11 2012-06-23 19:08:47

lindah
Member
Registered: 2010-01-25
Posts: 121

Re: Stopping times

Thank for that bobbym!

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#12 2012-06-23 22:26:47

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Stopping times

Hi lindah;

Please let me know if you get anything.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#13 2012-06-23 23:37:24

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,153

Re: Stopping times

hi lindah and bobbym,

I wasn't going to get involved in this thread but I'm greatly encouraged that bobbym finds it incomprehensible too (Hope I'm reading you correctly there.  Apologies if not).

I looked up some stuff on Wiki and looked at that video.  I also looked at some of

http://www.youtube.com/watch?feature=en … PojY4&NR=1

and

http://www.youtube.com/watch?v=y4VFtCStgFI

I could write a book on how not to present an explanation on a video, but, nevertheless, I'm beginning to follow what this is on about.

So let's try to answer your original post.

What does

In this context, I think this means the minimum of tau a and tau b.

That symbol has many possible meanings but this is the only one that fits here.

http://en.wikipedia.org/wiki/List_of_ma … al_symbols

As times are measured positively from 0, that would just mean the earlier of the two times.

So tau a is the first time the variable reaches a and tau b is the first time the variable reaches b.

Can you decide you'll stop at the earlier of these two times?  Yes you can.  So it is a stopping time.

That's my take on it.  Don't know if it helps or is just a load of rubbish.  dunno

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#14 2012-06-24 00:20:51

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Stopping times

Hi Bob;

I'm greatly encouraged that bobbym finds it incomprehensible too

That encouragement will be shortlived when I tell you I have been

baffled by butter
bewildered by bananas
confused by cornflakes
dizzied by dumplings
confounded by crumpets
befuddled by broccoli
stunned by selzer
puzzled by pepperoni
muddled by meatballs...

Thanks for the videos, I will eat and watch them.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#15 2012-06-24 09:48:50

lindah
Member
Registered: 2010-01-25
Posts: 121

Re: Stopping times

Hi bob and bobbym;

Thank you for that! I just confirmed with my tutor that bob's answer is the right one. I had no idea what that wedge symbol meant, but in this context it definitely means the minimum as bob has identified.

Oh my, another piece of the puzzle in place smile

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#16 2012-06-24 10:00:38

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Stopping times

Hi lindah;

I did not do anything except eat and watch 2 videos.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#17 2012-06-24 18:18:19

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,153

Re: Stopping times

hi lindah,

Thanks for letting us know.  I have learnt a little more maths so it's been an interesting journey.  smile

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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