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Results tagged with probability-distributions
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user 157982
In probability and statistics, a probability distribution assigns a probability to each measurable subset of the possible outcomes of a random experiment, survey, or procedure of statistical inference.
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Is the topology generated by the convergence of finite-dimensional distributions metrizable?
Let $\mathbf{D} := D([0,1]; \mathbb{R}^d)$ be the Skorokhod space (equipped with the Skorokhod metric) of càdlàg functions, and let $X = (X_t)_{t \geq 0}$ be its canonical process. The space of probab …
- 309
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About the metrizability of the space of Probability measures $\mathcal{P}(S)$
It is often proved in Books that the space of Probability measures $\mathcal{P}(S)$ on a Polish metric space $(S,\rho)$ endowed with the weak/narrow topology induced by declaring it to be be the coars …
- 309
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Continuous version of conditional probability distributions $( \mathcal{L}(X_t | \mathcal{G}...
Let me first explain the setup:
Let $(X_t)_{t \geq 0}$ be a stochastic process on some probability space $(\Omega,\mathcal{F},P)$ with values in a complete and separable metric space $E$ (e.g. $E = \ …
- 309
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Can the joint law $P \circ (X,Y)^{-1}$ of two random variables $X$ and $Y$ be written as $P ...
I want to know whether there is some general assumpitons we can make on two measurable spaces $E$ and $F$ (e.g. polish, complete, separable,...) such that we can ensure that the following "Theorem" ho …
- 309