1
vote
0answers
26 views

How's the damping factor in Google PageRank algorithm calculated

I'm doing some researches about Google's PageRank algorithm for my thesis, I've found that the damping factor x (for example), where x is in : P` = x.P + (1-x)Q where P is the original ...
3
votes
1answer
59 views

Random walk where increment depend on current position

Consider the following stochastic process, $$b(i+1) = b(i) + \xi_i (b_i),$$ where $\xi_i(b_i) \in \{-1, k \}$ are the independent increments having the following distribution: $$\begin{align} P (\xi ...
5
votes
1answer
111 views

Log-likelihood function

I'm not sure if this could be asked here, or in math overflow... In the following paper Cho, Jin Seo, and Halbert White. "Testing for regime switching." Econometrica 75.6 (2007): 1671-1720. doi: ...
1
vote
2answers
182 views

Diffusion process. Distribution vs transition probability.

I need confirmation on the following problem: Take a SDE of the form: \begin{equation} dX_t=a(X_t,t)dt+b(X_t,t)dW_t \end{equation} where all the conditions, such that the solution $X_t$ is defined ...
0
votes
0answers
50 views

Variability in estimations over a non-ergodic/non-regular Markov process

Imagine we have a non-ergodic/non-regular Markov Process with with $n$ states. Among these $n$ states, there are $k$ absorbing states. For each of the $n-k$ non-absorbing states, it is not possible ...
1
vote
0answers
28 views

Single evaluation for using exponential sampling until past a point

I am trying to improve an algorithm that looks like the following (and am getting stumped): I am provided with a starting time, rate, and a target time. I then use an exponential distribution to ...
0
votes
2answers
47 views

How do you explain $f(x_4|x_3)f(x_3|x_2)f(x_2|x_1)f(x_1) = f(x_4,x_3,x_2,x_1)$?

Let $x_1=x(n_1)$, $x_2=x(n_2)$, $x_3=x(n_3)$ and $x_4=x(n_4)$ be random Markov processes $(n_1 < n_2 < n_3 < n_4)$. I don't understand the identity given below on their probability density ...
0
votes
1answer
103 views

Reversibility of Markov Process and Exponential Distribution of Transition Rates

I am reading the paper Towards Utility-optimal Random Access Without Message Passing by J. Liu, Y. Yi, A. Proutiere, M. Chiang, H. V. Poor. A sentence in Section 3.2 can be paraphrased as follows: ...