Bounded integrable functions

lindah · 2012-06-25 00:45:47

Hi guys,

Sorry for the raft of questions, my exam is in a couple of days and I think my brain has imploded, so apologies if this is a very silly question
Currently I am assessing whether the Radon-Nikodym derivative is a martingale. A sufficient condition (Novikov's) for this is:

Does this condition simply requires the function to be finite. I've always taken this definition (integrable functions) for granted, and have never needed analysis until now.

For example if the expectation I obtain is

then this is not ?

Thank you in advance for any feedback

Last edited by lindah (2012-06-25 00:46:05)

lindah · 2012-07-02 22:18:54

Thanks to bobbym, bob bundy and gAr for your help with my questions recently!!

My exams have finished and I'll know results in a couple of weeks

Linda

bobbym · 2012-07-02 23:41:51

Hi lindah;

I remember reading that Girsanov's theorem says that sometimes that is a Martingale.

lindah · 2012-07-03 00:14:56

Hi bobbym,

The Radon-Nikodym always has to be a martingale for Girsanov's change of measure to be valid w.r.t Brownian motion.

bobbym · 2012-07-03 00:21:45

Hi;

How would you get e^(ax)? Where does the a come from?

lindah · 2012-07-03 00:57:05

Hi bobbym;

I made up the e^ax, the a is supposed to be a constant

bobbym · 2012-07-03 01:00:02

Then I would assume that it is less then infinity. The integral is said to exist and is thus a Martingale. The H(s) would also have to reduce to a constant? So shouldn't that be an indefinite integral?

Math Is Fun Forum

#1 2012-06-25 00:45:47

Bounded integrable functions

#2 2012-07-02 22:18:54

Re: Bounded integrable functions

#3 2012-07-02 23:41:51

Re: Bounded integrable functions

#4 2012-07-03 00:14:56

Re: Bounded integrable functions

#5 2012-07-03 00:21:45

Re: Bounded integrable functions

#6 2012-07-03 00:57:05

Re: Bounded integrable functions

#7 2012-07-03 01:00:02

Re: Bounded integrable functions

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