Suppose we have two probability measures on $R^2$ $\mu_1,\mu_2$. I am looking to construct a coupling $\pi$ on $R^3$ such that the $(x,y)$-marginal is $\mu_1$ and the $(y,z)$ marginal is $\mu_2$. Can we always construct such a coupling? Here when I specify the marginals, I am assuming the form $(x,y,z)\in R^3$. What are some conditions where I can and can't do this.
2026-02-23 08:28:36.1771835316
3 dimensional couplings
35 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in PROBABILITY-THEORY
- Is this a commonly known paradox?
- What's $P(A_1\cap A_2\cap A_3\cap A_4) $?
- Another application of the Central Limit Theorem
- proving Kochen-Stone lemma...
- Is there a contradiction in coin toss of expected / actual results?
- Sample each point with flipping coin, what is the average?
- Random variables coincide
- Reference request for a lemma on the expected value of Hermitian polynomials of Gaussian random variables.
- Determine the marginal distributions of $(T_1, T_2)$
- Convergence in distribution of a discretized random variable and generated sigma-algebras
Related Questions in INDEPENDENCE
- How to prove mutually independence?
- Simple example dependent variables but under some conditions independent
- Perturbing equivalent measures
- How to prove conditional independence properties
- How do I prove A and B are independent given C?
- Forming an orthonormal basis with these independent vectors
- Independence of stochastic processes
- joint probability density function for $ X = \sqrt(V) \cdot cos(\Phi) $ and $ Y = \sqrt(V) \cdot sin(\Phi) $
- How predictable is $Y$, given values of $X_i$s?
- Each vertex of the square has a value which is randomly chosen from a set.
Related Questions in COUPLING
- How to uncouple and reduce/solve a system of 2nd order PDEs
- Showing that the balls respect to Wasserstein metric with equal radius in $\mathcal{P}_{p}(\Xi)$ and $\mathcal{P}(\Xi)$ respectively are equal.
- Trying to Understand Coupling Arguments Through a Simple Markov Chain Example
- Proof for total variation distance for product measure using coupling
- Coupling two random variables
- Coupling via push-forward from a source space
- Realize a coupling in the target space via a measure on the source space
- How does Markov Chain coupling work?
- Give a coupling under which a random variable dominates another random variable
- Successful couplings and total variation convergence to equilibrium for time-homogeneous Markov processes
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?