2
votes
1answer
35 views

Skorohod convergence (space of right continuous functions with left limit)

If $f_n$ is a sequence of functions of the Skorohod Space $D([0,\infty),E)$, where $E$ is a separable Banach space, such that $f_n \to f$ in the Skorohod topology. Is it possible that there exists a ...
0
votes
0answers
18 views

Are there “necessary” conditions for a solution to the multivariate, truncated Hausdorff moment problem?

I am looking for NECESSARY conditions for a solution to the multivariate, truncated Hausdorff moment problem (i.e., conditions under which a given finite sequence of numbers is the sequence of first ...
1
vote
0answers
50 views

Banach space :space of all adapted processes continuous equipped wih specific norm is complete

Let $\mathbb{B}$ be space of all adapted processes continuous equipped with the norm $\lVert Y\rVert_{\mathbb{B}}^2=E\left[\sup_{t\in [0,T]} |Y_{t}|^{2}\right] < \infty $, ...
0
votes
1answer
94 views

How to show Wiener measure induces basic properties of Brownian motion?

page 19 of http://www.math.tifr.res.in/~publ/ln/tifr64.pdf gives a defintion of Wiener measure Ft1,t2,..,tk. But how can we show it is a probability measure and it satisfies the consistency condition ...
4
votes
0answers
219 views

Can infinitesimal generator be defined by the time-inhomogeneous stochastic process?

The following is the definition of infinitesimal generator from Oksendal. Let $\{X_t,t\in[0,T]\}$ be a time-homogeneous It\^o diffusion in $\mathbb{R}^d$. The $\textit{infinitesimal generator}$ ...
0
votes
0answers
84 views

How Wiener Measure on $F(C([0,T]))$ is a Gaussian Measure

I'm looking for some simple proofs for the fact that on $(C[0,T],F(C([0,T])),P_{*})$ where $F$ represents Borel Sigma algebra , $P_{*}$ the Wiener Measure , then how to proove that $P_{*}$ measure is ...