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. …

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 …

(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 …

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 …

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 …

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

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 …

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 …

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(\ …

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 …

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 …

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 …

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 …

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 …

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 …