I'd like to have an example of a stationary process $(X_n)_{n \in \mathbb{Z}}$ on a finite alphabet for which the shift $T$ is ergodic and has discrete spectrum, and for which there is a "nice" description of the law of $(X_n)_{n \in \mathbb{Z}}$, for example a simple expression for the transition probabilities $\Pr(X_{n+1}=x \mid X_m, m\leq n)$.
2026-03-26 16:08:45.1774541325
nice stationary process with discrete spectrum
38 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 ERGODIC-THEORY
- the mathematics of stirring
- Kac Lemma for Ergodic Stationary Process
- Ergodicity of a skew product
- Is every dynamical system approaching independence isomorphic to a Bernoulli system?
- Infinite dimensional analysis
- Poincaré's Recurrence Theorem
- Chain recurrent set is the set of fixed points?
- Is this chaotic map known?
- A complex root of unity and "dense" property of the its orbit on the unit circle
- Books on ergodic operators
Related Questions in STATIONARY-PROCESSES
- Is $X_t$ a wide-sense stationary process?
- Absorbing Markov chain and almost sure convergence
- Mean value of a strict-sense stationary stochastic process
- Stationarity of ARMA model
- The Law of Total Covariance on a Gaussian Process
- application of Markov Chain and stationary distribution
- (Weak) Convergence of stationary distributions under tightness
- Durrett Stationary sequence counterexample
- Showing $\lim\limits_{R \uparrow \infty} \frac{1}{R^3} \int_{-R}^R \psi^2 (w,x) \, dx = 0$
- Weak stationarity for a stochastic process $\{X(t) \}$
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?