All Questions
Tagged with statistics stochastic-processes
713
questions
2
votes
2
answers
210
views
sub martingales and more
This is a problem on sub-martingales.
Given : $X_n = X_0 \mathrm{e}^{\mu S_n}$, $n= 1,2,3,\ldots$, where $X_0 > 0$ and
where $S_n$ is a symmetric random walk and $\mu$ is greater than zero.
We ...
- 36.2k
3
votes
1
answer
690
views
Birth-death process invariant distribution
Let $X_n$ be a birth-death process, with birth rates $\lambda_n$ and death rates $\mu_n$ (with $\mu_o=0$ and $\lambda_{-1}=0$). How do you show that the invariant distribution $\pi_i$ is:
$\pi_0=\Big[...
- 159k
2
votes
0
answers
276
views
Orthant probability / passage-time [closed]
I'm having a hard time solving this problem. Would appreciate any hint! (and special thanks to Byron Schmuland for answering my previous 2 questions. This 3rd question is different.)
Let $e_t$: $e_1$...
CommunityBot
- 1
4
votes
1
answer
2k
views
Questions about geometric distribution
I have some trouble understanding the record value for a sequence of i.i.d. random variables of geometric distribution. Following quotation is from Univariate discrete distributions By Norman Lloyd ...
- 26.4k
2
votes
1
answer
360
views
MCMC Metropolis Hastings
Does anyone know a webpage or a document where I can find a practical example of implementation of the Metropolis-Hastings algorithm, with some thoughts about burn-in time and how to construct the ...
CommunityBot
- 1
2
votes
1
answer
853
views
posterior distribution after having partial information on some linear combinations of unknown variables (Revised)
$x_1$, $x_2$, and $x_3$ are i.i.d. normal random variables with distribution $N(0, \sigma_x^{2})$
$\epsilon_1$, $\epsilon_2$, and $\epsilon_3$ are i.i.d. normal random variables with distribution $N(...
CommunityBot
- 1
1
vote
2
answers
503
views
Stochastic Urn Process using a Pareto distribution
N urns are assigned m balls in a stochastic process based on a Pareto distribution. The process is as follows:
X is a Pareto random variable (xminimum = 1, alpha is a parameter)
if X > N, throw the ...
CommunityBot
- 1
1
vote
1
answer
119
views
n agents accessing a resource
I want to solve a simple stochastic problem. Imagine there are n agents who want to access a resource, with a probability p at a given time t. What ist the probability that the resource will be free ...
CommunityBot
- 1