Why is the random walk on $R^d$ a time-homogeneous markov chain?
Feb 9, 2026 · I am referring to this question: Why is a random walk a time-homogeneous Markov process? I would like to know: Why is the time-homogeneous markov property (requirement 3 in the …
stochastic processes - Mathematics Stack Exchange
Sep 30, 2023 · What is the difference between a Gaussian random walk and a Gauss-Markov process? Ask Question Asked 2 years, 4 months ago Modified 2 years, 4 months ago
probability theory - Question about the definition of Markov kernel ...
Dec 8, 2022 · To sum up, Markov kernels are a formal way to set up conditional distributions. (2) is precisely the part of the definition that captures this aspect, while (1) is needed for technical reasons …
What is the difference between all types of Markov Chains?
Apr 25, 2017 · A Markov process is basically a stochastic process in which the past history of the process is irrelevant if you know the current system state. In other words, all information about the …
Ergodic Markov chains and the ergodic theorem
Sep 27, 2024 · This mapping between deterministic systems and Markov chain is a useful bridge. For example in the study of dynamical systems, this allows you to reduce the study of chaotic maps to …
probability - What is the steady state of a Markov chain with two ...
Feb 27, 2024 · The time it spends in each state converge to $\frac12$, but the probability to be in a state is entirely determined by whether the time is even or odd. A Markov chain on a finite space is called …
Action of a toral automorphism on a Markov partition
May 14, 2020 · Action of a toral automorphism on a Markov partition Ask Question Asked 5 years, 9 months ago Modified 5 years, 9 months ago
Intuitive meaning of recurrent states in a Markov chain
Jun 6, 2025 · In a Markov process, a null recurrent state is returned to, but just not often enough for the return to be classified as periodic with any finite period. (eg. returning, on average once every 4.5 …
probability - Is the Markov property equivalent to the statement "past ...
Jul 27, 2023 · It is easy to show that the Markov property implies that "past and future are independent given the present". Is if the reverse implication also true (as John Dawkins's answer to this question …
Proving The Fundamental Theorem of Markov Chains
Apr 14, 2024 · Theorem 1 (The Fundamental Theorem of Markov Chains): Let $X_0, X_1, \ldots$ be a Markov chain over a finite state space, with transition matrix $P$. Suppose that the chain is …