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by Edophokles
May 11th, 2019, 5:29 am
Forum: Numerical Methods Forum
Topic: Why the minimum is taken here when its derivative > 0?
Replies: 2
Views: 678

Re: Why the minimum is taken here when its derivative > 0?

Hi EdisonCruise, 

what is the meaning of [$]\nu^{*}[$] in the paper?
by Edophokles
August 3rd, 2018, 7:10 am
Forum: Technical Forum
Topic: Does Cov(X,I{Y>K}) = Cov(X,Y|Y=K)f_Y(K) hold in general?
Replies: 4
Views: 534

Re: Does Cov(X,I{Y>K}) = Cov(X,Y|Y=K)f_Y(K) hold in general?

Well, your first equation holds in general only for a non-negative random variable Y and the integral should go from 0 to +infinity . And the second equation does not hold at all (unless X and Y are uncorrelated), since the term   Cov(X,Y|Y=K)  would always be zero. One of the ways to think about i...
by Edophokles
June 18th, 2018, 3:41 pm
Forum: Student Forum
Topic: Are these two RVs independent?
Replies: 15
Views: 998

Re: Are these two RVs independent?

I think, unfortunately neither of the statements can be proved for general \(x_t\). Consider a trivial example of any deterministic process \(x_t\). Then the random variables \(Z_T\) and \(Y_T\) are independent (and hence the expectation of the product of these random variables becomes zero due to \...
by Edophokles
June 18th, 2018, 8:47 am
Forum: Student Forum
Topic: Are these two RVs independent?
Replies: 15
Views: 998

Re: Are these two RVs independent?

Okay, in that case \( Y_T \) can be dependent on the whole information till time \(T \) by definition. Here, some simple example, \(\int_1^2B_tdt\) is not independent of \(B_{0.5} \).
by Edophokles
June 18th, 2018, 6:26 am
Forum: Student Forum
Topic: Are these two RVs independent?
Replies: 15
Views: 998

Re: Are these two RVs independent?

What do you actually mean by E_T and E_t? Is it the conditional expectation given all the information generated by W_s  till the time T and t, respectively?
by Edophokles
January 30th, 2018, 8:10 am
Forum: Technical Forum
Topic: Compound Poisson Process
Replies: 4
Views: 555

Re: Compound Poisson Process

The second equation (1.23) is simply the differential notation of the integral form.  The first one (1.22) is due to the fact that a Poisson process only changes when it jumps, hence d π ( s )  is zero everywhere except when the jump occurs, then it is 1. Thus, the integral simply becomes the sum of...
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