# Questions tagged [random-functions]

This tag is for questions relating to the functions of random variables which is a function from $Ω$ into a suitable space of functions (where $Ω$ is the sample space of a probability space that has been specified). Technically, there is also a measurability condition on this function.

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### Characteristic function of the mean of a Dirichlet process

In a 1984 paper discussing the characteristic function of the mean of a random distribution driven by a Dirichlet process ${\sf DP}(M,G_0)$ (Ferguson, 1973), $M>0$, Hajime Yamato sets a constraint ...
1 vote
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### Uniformly simulating random functions with derivative bounded by fixed constant

I want to be able to uniformly draw (finite approximations of) functions $f: [0,1] \to \mathbb{R}$ such that $f(0)=a$, $f(1)=b$, and $|f'(x)|<s$ (for a fixed $s$). I want to do this so I can draw ...
1 vote
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### If Z=X+Y for random variables X and Y, can I transform X and Y once I derive the distribution of Z?

I am trying to derive the distribution of $Z = X + Y$, where $X$ and $Y$ are normally distributed and but not necessarily independent random variables. To make the math easier, I started by ...
113 views

### Under what conditions will the variance of max(X,Y) be greater than max(X-Y,0), if X and Y are random variables?

This is a bit of an open-ended question that's been bugging me for a while, and any help or insight would be appreciated. My apologies in advance if I make any math sins, please correct me if so. ...
1 vote
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### Measurability of (random) set valued functions

Consider the following problem. Given a set $A\in \mathcal{B}(\mathbb{R})$, we have the associated indicator function $1_A(x) \in L^\infty(\mathbb{R})$, is this mapping, $A\mapsto 1_A$ in some sense ...
1 vote
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### Is it possible for me to derive a function that uses a random integer to derive a pseudorandom number from an indexed list of sequential numbers?

Assuming I have one random integer, let's say 123456, and an indexed list of numbers [1, 2, 3 ... 100] Is it possible for me to derive a function that uses the random integer to derive a pseudorandom ...
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### How can we demonstrate that the local variance tends to increase with local mean for a random field obeying lognormal distribution?

In the classic geostatistics book "Goovaerts,P., 1997. Geostatistics for natural resources evaluation. Oxford University Press", it said that "For positively skewed distributions, the ...
1 vote
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### Whether the autocorrelation structure of random field $Z(u) + Y(u)$ is equal to the autocorrelation structure of $Z(u)$ plus that of $Y(u)$?

I want to simulate a Gaussian random field (RF) with correlation structure (represented by the geostatistic tool 'semivariogram' $\gamma (h) \: +\: pure \: nugget \: effect$). I want to know whether ...
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### 2D space and 1D time evolution of a random field

I want to develop a 2D random field and its change with time with constant velocity. My process: Define a 2D grid (not the fields yet) $[x, y]$ with $n \times n$ points Define 1D time axis $[t]$ with ...
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### Maxima/minima of a random curve

Let $\left\{ {{\xi _k}} \right\}$ be independent random variables with some known distribution function ${F_\xi }$ and $f(x)$ be a "good" function that is bounded and decrease to zero with ...
1 vote
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