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Random Walk Randomly Reflected

Hi I am not specialist in probability so I will not be surprised if the answer for this question is just a simple consequence of well known results from the random walk theory. In this case, I will ...
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Counting of brownian particles: Point Process

Imagine a point process defined by the passage time of purely brownian particles through a given point (in 1D), line (2D) or plane (3D). I'm interested in the variance of the counts (number of ...
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What is the probability density function over time for a 1-D random walk on a line with boundaries?

If a single particle sits on an infinite line and undergoes a 1-D random walk, the probability density of its spatio-temporal evolution is captured by a 1-D gaussian distribution. \begin{align} P(x,t)...
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What is corresponding fokker planck equation for, $\frac{df(t)}{dt}=-kf(t)+\zeta(t)$ where, $\zeta(t)$ is random noise. In particular, how will the fokker planck equation will look like if $\zeta(t)... 1answer 105 views Rate of probability loss from absorbing boundary The following is the solution to the 1D diffusion equation with diffusion coefficient D, initial particle position$x_0$, and a perfectly absorbing boundary at$x=0$(s.t.$P(x=0)=0$). $$P(x;t)=\... 1answer 339 views Describe Ising model dynamics in stochastic differential equation or stochastic process The Ising model is described by the Hamiltonian$$ H(\sigma) = - \sum_{<i~j>} J_{ij} \sigma_i \sigma_j -\mu \sum_{j} h_j\sigma_j, $$and is treated extensively by equilibrium statistical ... 1answer 59 views bimolecular reaction master equation I was wondering how to write down the deterministic rate equation for a bimolecular reaction with similar particles. e.g. A \rightarrow^{k_+} B +B and B +B \rightarrow^{k_-} A now the rate ... 1answer 46 views How to add Langevin terms to the semiclassical Bose-Hubbard model? I would like to add Langevin terms to the Hamilton equations of motion of the semiclassical Bose-Hubbard model. Here's what I have: I start with the standard example of Brownian motion, a particle ... 1answer 37 views From exponential distribution to Poisson distribution We know that the exponential distribution characterises the probability distribution for the waiting time between two consecutive Poisson events. Then I think if we fix a time interval T then we ... 1answer 760 views Autocorrelation and Power density spectrum : Continuous Markov Process I've been reading through the paper from Gillespie on Brownian motion and Johnson Noise (DOI, PDF). He considers X_s(t), a zero-mean stochastic variable, that is stationary in the sense that all of ... 0answers 51 views Quantum mechanics - “God does not play dice” - does he? Or might he not? [duplicate] I'm a mechanical engineer by training, so please forgive ignorance in my question. Heisenberg's uncertainty principle states (to my understanding) that one cannot measure both position and momentum ... 1answer 40 views Karhunen-Loeve transform of a repeating process This question is inspired by measurements of an unsteady flow. I have some doubts about interpretation of principal component transform using Karhunen-Loeve theorem. I have (centered \equiv zero ... 2answers 111 views Resources on Master Equations Presently I am reading about "Introduction to dynamical process theory and simulation" which uses the notion of Master Equations to solve Markov process. I am very new to this. Can someone provide me ... 1answer 26 views 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 ... 1answer 123 views Is this hypo-theoretical model of future prediction feasible? [closed] First let me state that I am not, nor ever have I been, a physics student. I am working on an idea for a book I'm writing. This is a thought experiment that posits the existence of a computer system ... 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 ... 1answer 58 views Detailed balance of an energy function I'm having difficulties understanding a problem about the acceptance rules for a given energy landscape. The Problem Suppose a system in which the energy is a function of x only:$$ e^{-\beta U(x)} =... 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 ...