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Jan
16
asked Laurent expansion of $1/(1+z^n)$ for $n \in \mathbb{N}$.
Jan
13
accepted Let $f(x) = (x^n-1)/(x-1)$. Why does $f(1)=n$?
Jan
13
comment Let $f(x) = (x^n-1)/(x-1)$. Why does $f(1)=n$?
See my edit to the original post. $f$ is defined as a polynomial so I think you are right in that in order for $f$ to be a polynomial, it must be defined that $f(1)=n$.
Jan
13
revised Let $f(x) = (x^n-1)/(x-1)$. Why does $f(1)=n$?
added 269 characters in body
Jan
13
asked Let $f(x) = (x^n-1)/(x-1)$. Why does $f(1)=n$?
Jan
3
comment Let $f(z) = \frac{z^{-2}}{\sin( \pi z )}$. What is the residue for $z \neq 0$?
Thank you for the clarification. Understood
Jan
2
comment Let $f(z) = \frac{z^{-2}}{\sin( \pi z )}$. What is the residue for $z \neq 0$?
Could you expand on how you know the value of the coefficient in your second to last sentence from the right side of the equality? I don't know how to perform a Laurent expansion on your result.
Jan
2
accepted Let $f(z) = \frac{z^{-2}}{\sin( \pi z )}$. What is the residue for $z \neq 0$?
Jan
1
asked Let $f(z) = \frac{z^{-2}}{\sin( \pi z )}$. What is the residue for $z \neq 0$?
Dec
20
revised What is the formula for a likelihood ratio $L$ that transforms martingale Geometric BM to Geometric BM with positive growth?
added 420 characters in body
Dec
20
asked What is the formula for a likelihood ratio $L$ that transforms martingale Geometric BM to Geometric BM with positive growth?
Dec
19
accepted What is the statistical steady state of this poisson process?
Dec
18
comment What is the statistical steady state of this poisson process?
Thanks, that would be helpful so that I can review your answer again in more detail.
Dec
18
comment What is the statistical steady state of this poisson process?
Also, I'm a little unsure of how you derived the balance equation?
Dec
18
comment What is the statistical steady state of this poisson process?
how did you arrive at the mass functions as functions of time "i", $\lambda / (\lambda + i \mu)$ and $i \mu / (\lambda + i \mu)$? I don't have this in my answers.
Dec
18
comment What is the statistical steady state of this poisson process?
@A.S. I'd like to understand both your approaches. How do you arrive at a rate of change of $n$ people of $\lambda - n \mu$? On your first comment, what is the equation that signifies zero change of probability density? If this is the density of the number of people on the island, how do you find that density from the given processes?
Dec
18
asked What is the statistical steady state of this poisson process?
Dec
18
accepted Suppose $dX_t = a(X_t) dt + b(X_t) dW_t$ and $Y_s=X_t$ where $s=t^2$. What SDE does $Y_s$ satisfy in the weak sense?
Dec
16
comment Suppose $X_{n+1} = 2X_n - X_{n-1} + Z_n$. What is the value function and backward equation to calculate $P(X_T > 1 \mid X_0 = X_1 = 0)$.
@A.S. that makes a lot of sense. Thanks for the remark. Although does that get us anywhere in terms of understanding how to use a value function and backward equation to solve the question? I'm doing this as practice and would like to understand the question using the method as stated. Appreciate your remarks though.
Dec
16
asked Suppose $X_{n+1} = 2X_n - X_{n-1} + Z_n$. What is the value function and backward equation to calculate $P(X_T > 1 \mid X_0 = X_1 = 0)$.