Three examples of Brownian flows on $\RR$

Details Three examples of Brownian flows on $\RR$ Three examples of Brownian flows on $\RR$

2011-11-08

arxiv.org/abs/1111.1846v1

Mathematics

Probability

32 pages

Scientific paper

We show that the only flow solving the stochastic differential equation (SDE) on $\RR$ $$dX_t = 1_{\{X_t>0\}}W_+(dt) + 1_{\{X_t<0\}}dW_-(dt),$$ where $W^+$ and $W^-$ are two independent white noises, is a coalescing flow we will denote $\p^{\pm}$. The flow $\p^\pm$ is a Wiener solution. Moreover, $K^+=\E[\delta_{\p^\pm}|W_+]$ is the unique solution (it is also a Wiener solution) of the SDE $$K^+_{s,t}f(x)=f(x)+\int_s^t K_{s,u}(1_{\RR^+}f')(x)W_+(du)+(1/2) \int_s^t K_{s,u}f"(x) du$$ for $s

Affiliated with

Also associated with

No associations

Rating

Three examples of Brownian flows on $\RR$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Three examples of Brownian flows on $\RR$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Three examples of Brownian flows on $\RR$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-53350