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Aug
6
awarded  Yearling
Aug
5
awarded  Popular Question
May
13
comment Does the random variable $f(\tau)M_\tau$, where $M$ is a martingale and $\tau$ is a stopping time, have zero expectation?
It ok, you are right, it is hard to answer. I was hoping this may be a standard result that someone would recognise. Thanks for the effort anyway.
May
12
comment Does the random variable $f(\tau)M_\tau$, where $M$ is a martingale and $\tau$ is a stopping time, have zero expectation?
@Michael, You are right, "is it ever the case" is ambiguous, and yes you can clearly find easy cases. I really meant something like is it true if the conditions for optional sampling are satisfied or some tweaked version of them?
May
12
comment Does the random variable $f(\tau)M_\tau$, where $M$ is a martingale and $\tau$ is a stopping time, have zero expectation?
Hey, the time to award the bounty was running out, so I just awarded it to the only answer; yours. Thank you for replying in the first place.
May
3
comment Does the random variable $f(\tau)M_\tau$, where $M$ is a martingale and $\tau$ is a stopping time, have zero expectation?
@Slungpue Yes, I know, but do you have any suggestions how to proceed from there?
May
3
comment Does the random variable $f(\tau)M_\tau$, where $M$ is a martingale and $\tau$ is a stopping time, have zero expectation?
I agree, this won't hold in general. But I'm wondering if it does under conditions similar to those needed for optional sampling.
May
3
asked Does the random variable $f(\tau)M_\tau$, where $M$ is a martingale and $\tau$ is a stopping time, have zero expectation?
May
2
answered Can an indicator function be a valid Radon Nikodym derivative?
Apr
18
answered Expectation of minimum discrete and continious random variable
Apr
18
comment Borel Measurable Function 3
Yes, but note that you also need $X$ to be a topological space in order for the Borel sigma algebra (the sigma generated by the open sets) to be defined.
Apr
18
answered $\arg\max$ of an increasing function grows as the region grows.
Apr
18
answered Reasoning behind method of steepest descent
Apr
18
comment Finding a One Step Transition Matrix for a Markov Process? (Gambling Application)
To set up the transition matrix you need to describe the gambling itself (Is it a a toss of a fair coin, a slot machine with $N$ different outcome and probabilities $\mu(n)$ of outcome $n$, etc?
Apr
18
answered non-stationary Markov chain n-step
Apr
18
comment Book recommendation needed: asymptotic behavior of non-stationary Markov chain
Continuous-time or discrete-time chains?
Feb
11
revised How to efficiently represent and manipulate polynomials in software?
added 428 characters in body
Feb
11
revised How to efficiently represent and manipulate polynomials in software?
added 256 characters in body
Feb
11
comment How to efficiently represent and manipulate polynomials in software?
Thank you, this is a nice and sound suggestion. As a attempt I've implemented something along these lines. I gave the bounty to Respawned Fluff because of his great references, hope you do not mind to much.
Feb
11
accepted How to efficiently represent and manipulate polynomials in software?