Explore: Markov Kernels

probability theory, a Markov kernel (also known as a stochastic kernel or probability kernel) is a map that in the general theory of Markov processes plays

subprobability kernels instead of probability kernels, or more general s-finite kernels. Also, one can take as morphisms equivalence classes of Markov kernels under

{\displaystyle \Omega } . The discriminator's strategy set is the set of Markov kernels μ D : Ω → P [ 0 , 1 ] {\displaystyle \mu _{D}:\Omega \to {\mathcal {P}}[0

measures or stochastic processes. The most important example of kernels are the Markov kernels. Let ( S , S ) {\displaystyle (S,{\mathcal {S}})} , ( T , T

the Markov kernels induced by the transitions of a Markov process, the Chapman-Kolmogorov equation can be seen as giving a way of composing the kernel, generalizing

_{x}[f(X_{1})].} For a Markov kernel p {\displaystyle p} with starting distribution μ {\displaystyle \mu } one can introduce a family of Markov kernels ( p n ) n ∈

Gauss–Markov theorem Gauss–Markov process Markov blanket Markov boundary Markov chain Markov chain central limit theorem Additive Markov chain Markov additive

stochastic matrix is a square matrix used to describe the transitions of a Markov chain. Each of its entries is a nonnegative real number representing a probability

probability measures which depend measurably on a parameter (giving rise to Markov kernels), or when one has probability measures over probability measures (such

theorem can be expressed as a categorical limit in the category of Markov kernels. Let ( X , A ) {\displaystyle (X,{\mathcal {A}})} be a standard Borel