Questions tagged [diffusion]

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245 views

What is tantile regression?

My question follows on this discussion of medials and tantiles vs medians and quantiles from earlier this year: When would we use tantiles and the medial, rather than quantiles and the median? As ...
3
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0answers
28 views

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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498 views

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 ...
2
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0answers
91 views

Carré du champ operator is a quadratic variation

Let $X_t$ be a real valued Markov process (starting at $x$) with generator $L$. Let $\Gamma(f)$ denote Carré du champ operator i.e. $L(f^2) - 2f \cdot L (f)$. As far as I know under suitable ...
2
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0answers
35 views

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 ...
2
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23 views

How to apply the diffusion maps when the matrix is PSD but not positivity preserving?

In order to apply the diffusion maps in a matrix $C\in\mathbb R^{n\times n}$ , that matrix must obey some restrictions, C is symmetric: $C_{ij} = C_{ji}$, C is positivity preserving (PP): $\forall ...
2
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0answers
63 views

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 ...
2
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0answers
279 views

How to simulate anomalous diffusion of a 1D point like particle?

I want to simulate 3 types of diffusion processes: normal diffusion $[\langle x^2(t)\rangle \propto t ]$. subdiffusion $[\langle x^2(t)\rangle \propto t^\alpha ; \alpha<1 ]$ superdiffusion $[\...
1
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0answers
10 views

Fit drift diffusion model with trial-type dependent input strength

I want to fit a drift diffusion model to a task which involves multiple decisions (n=400) between two different valuable choice options . I do understand how I would do that in general, also with the ...
1
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0answers
76 views

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 ...
1
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78 views

Computing properties of non-uniform random walk/diffusion

I have a lot of numerical data which I'm looking to characterise as a (possibly continuous) random walk with variable (in space) step size, for example, along $x$ between $-1$ and $1$ with a step size ...
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249 views

2 Dimensional Random Walk Simulation

I am trying to simulate random diffusion of particles using a random walk diffusion model. I have used probabilities of movement of particles in a 2D area, to be 1/4 in all 4 directions. The confusion ...
0
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0answers
20 views

How are differential equations and stochastic differential equations different?

In the simplest terms, how are differential equations and stochastic differential equations different? As far as I can tell, SDEs are PDEs or ODEs, where the derivative of some function wrt itself is ...
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21 views

Forecasting new product sales - pre launch

Product X is due to launch in 6 months time and I am looking for a method to estimate what the sales of this product could likely be in 3 years time. Product X belongs to a category of products for ...