Tagged Questions

5
votes
3answers
413 views

Blue and red balls puzzle

I was sent this puzzle and wondered if it is known or if its origin is known? (I see colored ball puzzles are also in vogue.) Consider a bag with $n$ red balls and $n$ blue balls. …
-1
votes
0answers
46 views

PROBLEM: estimating peak traffic on web site [closed]

Hi Everyone, I have a (simple?) question that I hope someone will find interesting enough to help me out with. A web site has currently 3,000 subscribers who generate a certain a …
4
votes
0answers
132 views

Inadmissibility of Simpson’s rule

(An earlier version of this at stackexchange got no answers.) Bayesianism says that all uncertainties, or at least all uncertainties about the truth or falsity of propositions, ca …
3
votes
2answers
151 views

Probability distribution for two-state system that depends on residence time

I am a statistical physicist, and I've come across a problem that I don't know how to solve. I believe my issue lies with how to formulate it mathematically. I'd be very grateful f …
3
votes
1answer
120 views

Optimizing a stochastic “flip and prune” procedure for selecting a subset of coins

I place some number of coins, $(c_1, ..., c_N) \in C$ on a table, where each coin is originally tails up. Let's call the "tails" state $0$ and the "heads" state $1$. I then perfo …
0
votes
1answer
266 views

Mathematical properties of financial prices

Prices of financial assets (stock-market prices or currency exchange rates) obviously resemble trajectories of stochastic processes. What is known about their mathematical prope …
16
votes
2answers
449 views

Age of Stochasticity?

One user on MSE made an interesting question, which was unanswered so I suggested him to post it here but he refused for personal reasons and said I could ask it here. The questio …
0
votes
0answers
45 views

Conditions for almost sure convergence of processes.

Suppose I have a sequence of (Markov) stochastic processes $\left\{X^n_t:n\in\mathbb N, t\in[0,T]\right\}$ constructed on a common probability space. None of my $X^n_t$ are contin …
5
votes
0answers
301 views

When is an ODE a good approximation to an SDE?

Suppose $X_t$ is a weak solution to a stochastic differential equation in the form $$d X_t = \sigma(X_t) d W_t + \lambda(X_t) dt$$ for smooth functions $\sigma: \mathbb R^d \to L(\ …
4
votes
2answers
76 views

Simulating random sequential adsorption in reverse

Please consider two processes: Process 1 - I simulate random sequential adsorption of discs on the unit square in the continuum limit, randomly selecting real number coordinates …
1
vote
0answers
80 views

Langevin equation with position-dependant damping: existence of an invariant measure?

The usual Langevin equation for a particle in a 1D harmonic potential $dq(t) = p(t)~dt$ $dp(t) = -q(t)~dt + a ~dW(t) - b~p(t)~dt$ admits as an invariant measure the Gibbs measur …
1
vote
2answers
73 views

Strictly positive definite autocovariance function of fGn

Hi, let $\gamma(k) = 1/2 (|k+1|^{2H} + |k-1|^{2H}-2|k|^{2H}),k\in\mathbb{Z},$ be autocovariance function of fractional Gaussian noise where $H\in(0,1)$ is parameter. I want to sh …
2
votes
1answer
64 views

“Trapping” of discs after random sequential adsorption

Imagine I perform Random Sequential Adsorption (RSA) of discs of some radius $r$ on $[0, 1]^2$, eventually covering the surface to some density $Q \leq 0.543$ with $N$ total discs …
0
votes
1answer
48 views

Random Sequential Adsorption of Discs on a Plane - What is the best known lowerbound for the number of circles (of some radius $r$) guaranteed to fit on $[0, 1]^2$?

Imagine I perform a random sequential adsorption (RSA) simulation for circles or discs of some radius $r \leq 1$ in $[0, 1]^2$ (I am open to changing this geometry to the unit circ …
2
votes
0answers
70 views

A simplified MCMC / MH algorithm. Are there known convergence results?

Hi, I hope this isn't too basic. We were working on a simulation using a Monte Carlo Within Metropolis algorithm and noticed that the whole thing could be expressed in the form bel …

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