Excursion Reflected Brownian Motions And Loewner Equations In Multiply Connected Domains

Details Excursion Reflected Brownian Motions And Loewner Equations In Multiply Connected Domains Excursion Reflected Brownian Motions And Loewner Equations In Multiply Connected Domains

2011-12-18

arxiv.org/abs/1112.4123v1

Mathematics

Probability

Scientific paper

Excursion reflected Brownian motion (ERBM) is a strong Markov process defined in a finitely connected domain $D \subset \C$ that behaves like a Brownian motion away from the boundary of $D$ and picks a point according to harmonic measure from infinity to reflect from every time it hits a boundary component. We give a new construction of ERBM using its conformal invariance and discuss the relationship between the Poisson kernel and Green's function for ERBM and conformal maps into certain classes of finitely connected domains. One important reason for studying ERBM is the hope that it will be a useful tool in the study of SLE in finitely connected domains. To this end, we show how the Poisson kernel for ERBM can be used to derive a Loewner equation for simple curves growing in a certain class of finitely connected domains.

Affiliated with

Also associated with

No associations

Rating

Excursion Reflected Brownian Motions And Loewner Equations In Multiply Connected Domains 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 Excursion Reflected Brownian Motions And Loewner Equations In Multiply Connected Domains, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Excursion Reflected Brownian Motions And Loewner Equations In Multiply Connected Domains will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-25754