can someone please tell me what an equilibrium probability in a markov chain is and what the relation between the equlibrium probability and equilibrium distribution is?
Thanks
2026-04-04 09:46:35.1775295995
Equilibrium probability in a markov chain
2k Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in PROBABILITY
- How to prove $\lim_{n \rightarrow\infty} e^{-n}\sum_{k=0}^{n}\frac{n^k}{k!} = \frac{1}{2}$?
- Is this a commonly known paradox?
- What's $P(A_1\cap A_2\cap A_3\cap A_4) $?
- Prove or disprove the following inequality
- Another application of the Central Limit Theorem
- Given is $2$ dimensional random variable $(X,Y)$ with table. Determine the correlation between $X$ and $Y$
- A random point $(a,b)$ is uniformly distributed in a unit square $K=[(u,v):0<u<1,0<v<1]$
- proving Kochen-Stone lemma...
- Solution Check. (Probability)
- Interpreting stationary distribution $P_{\infty}(X,V)$ of a random process
Related Questions in MARKOV-CHAINS
- Calculating probabilities using Markov chains.
- Probability being in the same state
- Random walk on $\mathbb{Z}^2$
- Polya's Urn and Conditional Independence
- Markov Chain never reaches a state
- Finding a mixture of 1st and 0'th order Markov models that is closest to an empirical distribution
- Find probability function of random walk, stochastic processes
- Generating cycles on a strongly connected graph
- Will be this random walk a Markov chain?
- An irreducible Markov chain cannot have an absorbing state
Related Questions in MARKOV-PROCESS
- Definition of a Markov process in continuous state space
- What is the name of the operation where a sequence of RV's form the parameters for the subsequent one?
- Given a probability $p$, what is the upper bound of how many columns in a row-stochastic matrix exceed $p$?
- Infinitesimal generator of $3$-dimensional Stochastic differential equation
- Controlled Markov process - proper notation and set up
- Easy way to determine the stationary distribution for Markov chain?
- Why cant any 3 events admit Markov Property?
- Absorbing Markov chain and almost sure convergence
- Transition probabilities for many-states Markov model
- How to derive a diffusion tensor and stationary states given a Markov process transition matrix?
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?
I'm guessing you are referring to what is more commonly known as a stationary distribution. Suppose you had a Markov chain $X_t$ for $t>0$. After it runs for a long time, you could take a look at its state, e.g. $X_{1000}$. What would that state be? Well, we don't know for sure, but there's a chance it's equal to $A$, another chance it's $B$, etc., i.e. it follows some random distribution probability. This is the stationary distribution, and is a vector of probabilities that sum to 1.
The point of a stationary distribution is that it's a limiting distribution; as $t$ tends to infinity, the distribution of states you might find yourself in (without knowing the immediate prior state) tends to some limit.
However, there is a caveat: the stationary distribution doesn't always exist.