The Strong Markov Property
ثبت نشده
چکیده
Throughout, X := {X ï¿¿ } ï¿¿≥0 denotes a Lévy process on R ï¿¿ with triple (ï¿¿ ï¿¿ σï¿¿ ï¿¿), and exponent Ψ. And from now on, we let {ï¿¿ ï¿¿ } ï¿¿≥0 denote the natural filtration of X, all the time remembering that, in accord with our earlier convention, {ï¿¿ ï¿¿ } ï¿¿≥0 satisfies the usual conditions. Definition 1. The transition measures of X are the probability measures P ï¿¿ (ï¿¿ ï¿¿ A) := P {ï¿¿ + X ï¿¿ ∈ A} defined for all ï¿¿ ≥ 0, ï¿¿ ∈ R ï¿¿ , and A ∈ ï¿¿(R ï¿¿). In other words, each P ï¿¿ (ï¿¿ ï¿¿ •) is the law of X ï¿¿ started at ï¿¿ ∈ R ï¿¿. We single out the case ï¿¿ = 0 by setting µ ï¿¿ (A) := P ï¿¿ (0 ï¿¿ A); thus, µ ï¿¿ is the distribution of X ï¿¿ for all ï¿¿ > 0. ï¿¿ Note, in particular, that µ 0 = δ 0 is the point mass at 0 ∈ R ï¿¿ .
منابع مشابه
Annotations of an Example That Markov Process Has No Strong Markov Property
In this paper, we discuss an incorrect example that a Markov process does not satisfy strong Markov property, and analyzes the reason of mistake. In the end, we point out it is not reasonable to define strong Markov property by using transition probability functions since transition probability functions might not be one and only.
متن کاملStrong Markov property of Poisson processes and Slivnyak formula
We discuss strong Markov property of Poisson point processes and the related stopping sets. Viewing Poisson process as a set indexed random field, we demonstrate how the martingale technique applies to establish the analogues of the classical results: Doob’s theorem, Wald identity in this multi-dimensional setting. In particular, we show that the famous Slivnyak-Mecke theorem characterising the...
متن کاملON THE INFINITE ORDER MARKOV PROCESSES
The notion of infinite order Markov process is introduced and the Markov property of the flow of information is established.
متن کاملMarkov property and Strong additivity of von Neumann entropy for graded quantum systems
It is easily verified that the quantum Markov property is equivalent to the strong additivity of von Neumann entropy for graded quantum systems. However, the structure of Markov states for graded systems is different from that for tensor-product systems which have trivial grading. For three-composed graded systems we have U(1)-gauge invariant Markov states whose restriction to the marginal pair...
متن کاملStrong and weak mean value properties on trees
We consider the mean value properties for finite variation measures with respect to a Markov operator in a discrete environnement. We prove equivalent conditions for the weak mean value property in the case of general Markov operators and for the strong mean value property in the case of transient Markov operators adapted to a tree structure. In this last case, conditions for the equivalence be...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011