Reflected Brownian motion in generic triangles and wedges

@article{Kager2004ReflectedBM,
  title={Reflected Brownian motion in generic triangles and wedges},
  author={Wouter Kager},
  journal={Stochastic Processes and their Applications},
  year={2004},
  volume={117},
  pages={539-549}
}
  • W. Kager
  • Published 1 October 2004
  • Mathematics
  • Stochastic Processes and their Applications
View PDF on arXiv
7 Citations
Background Citations
1
Methods Citations
1

7 Citations

Simulation of reflected Brownian motion on two dimensional wedges

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References

SHOWING 1-10 OF 18 REFERENCES

Reflected planar brownian motions, intertwining relations and crossing probabilities

Brownian motion in a wedge with oblique reflection at the boundary

This work is concerned with the existence and uniqueness of a strong Markov process that has continuous sample paths and the following additional properties: (i) The state space is an infinite…

Random planar curves and Schramm-Loewner evolutions

We review some of the results that have been derived in the last years on conformal invariance, scaling limits and properties of some two-dimensional random curves. In particular, we describe the…

Conformal restriction: The chordal case

We characterize and describe all random subsets K of a given simply connected planar domain (the upper half-plane Η, say) which satisfy the conformal restriction” property, i.e., K connects two fixed…

Intersection Exponents for Planar Brownian Motion

We derive properties concerning all intersection exponents for planar Brownian motion and we define generalized exponents that, loosely speaking, correspond to noninteger numbers of Brownian paths.…

Critical Exponents, Conformal Invariance and Planar Brownian Motion

In this review paper, we first discuss some open problems related to two-dimensional self-avoiding paths and critical percolation. We then review some closely related results (joint work with Greg…

SLE and Triangles

By analogy with Carleson's observation on Cardy's formula describing crossing probabilities for the scaling limit of critical percolation, we exhibit ``privileged geometries'' for Stochastic Loewner…

Values of Brownian intersection exponents, I: Half-plane exponents

Theoretical physics predicts that conformal invariance plays a crucial role in the macroscopic behavior of a wide class of two-dimensional models in statistical physics (see, e.g., [4], [6]). For…

Excursion decompositions for SLE and Watts' crossing formula

It is known that Schramm-Loewner Evolutions (SLEs) have a.s. frontier points if κ>4 and a.s. cutpoints if 4<κ<8. If κ>4, an appropriate version of SLE(κ) has a renewal property: it starts afresh…

Beta-gamma random variables and intertwining relations between certain Markov processes

In this paper, we study particular examples of the intertwining relation Qt? = ?Pt between two Markov semi-groups (Pt, t = 0) defined respectively on (E,e) and (F,F), via the Markov kernel ?: (E,e) ?…