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### Examining the presence of persistent domain from time series data

There are three variables, $X_t$, $Y_t$, and $Z_t$ that are dependent of each other, and I have the time series data of those variables from replicated experiments. The stochastic dynamics look quite ...
One way to generate Brownian motion is as follows: Define a waiting time probability distribution $\psi(t)$ and step length probability distribution $\lambda(x)$. Require also that $\langle \psi \... 0answers 96 views ### Reference for stochastic processes which helps moving from a basic level to a measure theory one I'm looking for a reference (books, notes, lectures) which helps a physicist to understand the language of measure theory in the context of stochastic processes (in particular markov chains). I've ... 0answers 22 views ### How is the conversion from an operator equation to a c-number stocastic differential equation justified? In many papers on laser dynamics theory, quantum Langevin equation of operators is converted to c-number stocastic differential equations, which is analyzed to obtain results. However, why this ... 0answers 25 views ### how to use generating function to solve coupled linear master equations? I am trying to solve a two dimensional continuous time and discrete state master equation. The master equation is linear and looks as follows,$\frac{\partial P_A(x,y,t)}{\partial t} = k_{11} P_A(x-1,...
The integral I have to solve is: $$I=\int\int d \mathbf{r}d \mathbf{r}' \frac{\Phi(\mathbf{r})\Phi(\mathbf{r}')}{|\mathbf{r}-\mathbf{r}'|}$$ It is a six-dimensional integral which I am going to ...