Titlebook: Denumerable Markov Chains; with a chapter of Ma John G. Kemeny,J. Laurie Snell,Anthony W. Knapp Textbook 1976Latest edition Springer Scienc

Ligament

Paul Turner,Glyn Volans,Heather Wisemanor Brownian motion and one for potentials—are mathematically equivalent. That is, the results of the two theories are in one-to-one correspondence and any proof of a result in one theory can be translated directly into a proof of the corresponding result in the other theory. In this chapter we shall

边缘带来墨水

Paul Turner,Glyn Volans,Heather Wisemanit disk of two-dimensional Euclidean space. In two-space the boundary of the disk—namely the circle .—has the property that there is a one-one correspondence between the non-negative harmonic functions . in the disk and the non-negative Borel measures . on the circle.

Muscularis

https://doi.org/10.1007/978-3-642-82595-8 non-negative superregular function is constant, and hence the representation of such functions degenerates. Moreover, since a recurrent chain is in every state infinitely often with probability one, an almost-everywhere convergence theorem is out of the question.

剧毒

https://doi.org/10.1007/978-3-642-82595-8in an arbitrary countable parameter set .. Roughly, a random field with denumerable state space . is described by a probability measure . on the space . = . of all configurations of values from . on the generalized time set .. In this chapter we discuss certain extensions of Markov chains, called .

Microgram

Denumerable Markov Chains978-1-4684-9455-6Series ISSN 0072-5285 Series E-ISSN 2197-5612

灌溉

烧瓶

Paul Turner,Glyn Volans,Heather Wisemanhat an arbitrary stochastic process may be considered as a process on a suitable . in which the outcome functions . are coordinate functions. We see, therefore, that in a sense no generality is lost by discussing Markov chains in terms of sequence space.

inhumane

https://doi.org/10.1007/978-1-349-13937-8nt chains begins with a charac­terization of finite-valued non-negative superregular measures and functions; the reader should turn back to Sections 1-6c and 1-6d for the terms referred to in what follows.

angina-pectoris

Paul Turner,Glyn Volans,Heather Wisemanit disk of two-dimensional Euclidean space. In two-space the boundary of the disk—namely the circle .—has the property that there is a one-one correspondence between the non-negative harmonic functions . in the disk and the non-negative Borel measures . on the circle.

大酒杯

https://doi.org/10.1007/978-3-642-82595-8 non-negative superregular function is constant, and hence the representation of such functions degenerates. Moreover, since a recurrent chain is in every state infinitely often with probability one, an almost-everywhere convergence theorem is out of the question.