Timeline for The existence of stationary measures for certain Markov process

6 events

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Jul 19, 2015 at 2:31	comment	added	Galor		Yes , the state space I care is just an interval $[a,b]$. The meaning of "recurrence" here, I use the Harris's definition:Suppose the Borel set generated by $[a,b]$ is B,and Lebegue measure is L, for $\forall E \in B,\forall x_{0} \in [a,b]$ and $L(E)>0$, there will be $P(x_{t} \in E infinitely many\|x_{0})=1$,then I call this process is positive recurrence.
Jul 18, 2015 at 23:44	comment	added	Nate Eldredge		For example, an iid sequence drawn from a continuous distribution does not satisfy them. Usually when dealing with continuous-state models, you have to introduce a topology on the state space to be able to say anything useful.
Jul 18, 2015 at 23:43	comment	added	Nate Eldredge		Maybe you can be more explicit about your definitions. Do you really want your state space to be completely general (e.g. any measurable space) or are you willing for it to be, e.g., standard Borel? And what do you want "positive recurrence" and "communication" to mean, exactly? If you mean "for all $x$ we have $E_x[\tau_x] < \infty$" and "for all $x,y$ we have $P_x(\tau_y < \infty) = 1$" then these are extremely strong assumptions that are probably not satisfied by very many useful examples.
Jul 18, 2015 at 12:20	history	edited	Galor	CC BY-SA 3.0	deleted 67 characters in body
Jul 18, 2015 at 10:27	history	edited	Galor	CC BY-SA 3.0	added 2 characters in body
Jul 18, 2015 at 10:05	history	asked	Galor	CC BY-SA 3.0