21 reputation
4
bio website
location
age
visits member for 2 years, 7 months
seen Nov 25 '12 at 0:46

Food~Math~Take a nap~start again


Sep
24
awarded  Autobiographer
Oct
28
awarded  Tumbleweed
Oct
22
comment Can infinitesimal generator be defined by the time-inhomogeneous stochastic process?
@NateEldredge Sorry to reply you late. I answered in the above two comments.
Oct
21
awarded  Editor
Oct
21
comment Can infinitesimal generator be defined by the time-inhomogeneous stochastic process?
the time-homogenous Cauchy in the comment means that the elliptic differential operater is independent of time.
Oct
21
comment Can infinitesimal generator be defined by the time-inhomogeneous stochastic process?
For a time-homogenous Markov process X_t, we define the infinitesimal generator as following: \mathscr{A}f(x)=\lim_{t\rightarrow 0}\frac{T_t f(x)-f(x)}{t}, where T_t is the semi-group associated with the transition probability function of X_t. For a time-inhomogenous Markov process, we define the infinitesimal generator by: \mathscr{A}_s f(x)=\lim_{t\rightarrow 0}\frac{T_{s,s+t}f(x)-f(x)}{t}, where T is the semi-group associated to the nonstationary transition probiblity function of X_t.
Oct
12
revised Can infinitesimal generator be defined by the time-inhomogeneous stochastic process?
edited tags
Oct
11
revised Can infinitesimal generator be defined by the time-inhomogeneous stochastic process?
I sort of figure it out. But it is raised another problem. I already added it as comment. Wish people could give me some idea.
Oct
11
comment Can infinitesimal generator be defined by the time-inhomogeneous stochastic process?
I think I figure it out. Those definitions are equivalent because when we define it by semi-group, we also require that it should be independent of time t. Therefore it is implicitly assumed that the infinitesimal generator should only work on time-homogeneous Cauchy. But it is raised a question that do we have a "similar" generator which could help us deal with time-inhomogenous Cauchy? So does anyone know the second question?
Oct
9
awarded  Student
Oct
9
asked Can infinitesimal generator be defined by the time-inhomogeneous stochastic process?