Questions tagged [diffusion]

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How to generate a log-linear frequency distribution of walk durations with a random walk?

Imagine that I have a random walk of n-individuals running to time t. There is a lower absorbing boundary z at which each individual stops walking when encountered. Steps are randomly drawn from any ...
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What is the likelihood function of the starting time of diffusion?

I need to find the likelihood that a set of molecules was instantaneously released at time $t_0$, say $t_0=0$. Toy System Example: Let $N$ be the set of molecules released from a specific point in a ...
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Diffusion tensor as a covariance matrix

TLDR: In nuclear magnetic resonance (NMR), to study molecular diffusion we assume that molecules displace in 3D space according to a trivariate gaussian distribution. The variables are then the ...
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What is the distribution of the peak time of the first hitting time process

I need to find the distribution of the random variable $T_{peak}$ where $T_{peak}$ represents the peak time of the first hitting time process. Detailed Explanation of the System: There are $N^{Tx}$ ...
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Stochastic Differential equation: CAPM

Let $R = (R_1, \dots , R_M)'$ denote a vector of excess returns of $M$ assets observed at $n$ time points, $0 < t_1 < t_2 < \cdots < t_n < T$, within a time span $T > 0$. We wish ...
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Increase the number of samples when the PDF is invariant

Background: $$\frac{\partial C}{\partial t} = D \frac{\partial^2 C}{\partial x^2}$$ is given by Fick's second law, in which $D$ is the diffusion coefficient. The solution to this equation (given the ...
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Why is the sample variance equal to the average sample size for random processes?

I am learning auto-correlation function for fluorescence correlation spectroscopy (FCS) on fcsXpert.com. The web page says: For random processes such as diffusion, the average of the square of the ...
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Distribution of the step size of diffusion in 3-dimensional space

I need to find the distribution of the random variable $$Y=\sqrt{X_1^2+X_2^2+X_3^2}$$ where $X_i\sim{\cal{N}}(0,\sigma^2)$ and $\sigma^2$ is related to diffusion coefficient. All $X_i$s are ...
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Diffusion coefficient from double-normal probability density function

The spread of individuals of species is often described by so-called dispersal kernels. The main parameter of spread is then often the variance defined as the average squared movement distance of a ...