Reflected Brownian motion with skew symmetric data in a polyhedral domain

DOI10.1007/BF00320328zbMath0608.60074MaRDI QIDQ1085898

Ruth J. Williams

Publication date: 1987

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

zbMATH Keywords

skew symmetry conditioncharacterization and invariant measures of certain reflected Brownian motionsdensity of an invariant measureunique stationary distribution

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Brownian motion (60J65) Diffusion processes (60J60)

Related Items (33)

Weak convergence of obliquely reflected diffusions ⋮ One-dimensional Brownian particle systems with rank-dependent drifts ⋮ Local time and excursions of reflected Brownian motion in a wedge ⋮ A phase transition behavior for Brownian motions interacting through their ranks ⋮ Brownian models of closed queueing networks with homogeneous customer populations ⋮ Reflected Brownian motion in a convex polyhedral cone: tail estimates for the stationary distribution ⋮ Long time behaviour and mean-field limit of Atlas models ⋮ Diffusions with rank-based characteristics and values in the nonnegative quadrant ⋮ Convergence rates for rank-based models with applications to portfolio theory ⋮ Strong solutions of stochastic equations with rank-based coefficients ⋮ Two Brownian particles with rank-based characteristics and skew-elastic collisions ⋮ Stochastic Games for Fuel Follower Problem: $N$ versus Mean Field Game ⋮ Competing particle systems evolving by interacting Lévy processes ⋮ Zipf’s law for atlas models ⋮ A combinatorial analysis of interacting diffusions ⋮ The Skorohod oblique reflection problem in domains with corners and application to stochastic differential equations ⋮ Brownian Motion in a Wedge with Variable Skew Reflection ⋮ Hybrid Atlas models ⋮ A time-reversed representation for the tail probabilities of stationary reflected Brownian motion. ⋮ Atlas models of equity markets ⋮ State space collapse and diffusion approximation for a network operating under a fair bandwidth sharing policy ⋮ Interlaced processes on the circle ⋮ On collisions of Brownian particles ⋮ Exponential ergodicity and convergence for generalized reflected Brownian motion ⋮ Characterization of stationary distributions of reflected diffusions ⋮ INFINITELY MANY BROWNIAN GLOBULES WITH BROWNIAN RADII ⋮ Brownian models of multiclass queueing networks: Current status and open problems ⋮ Sensitivity analysis for diffusion processes constrained to an orthant ⋮ Stationary distributions and convergence for \(M/M/1\) queues in interactive random environment ⋮ Penalty method for obliquely reflected diffusions ⋮ The infinite Atlas process: convergence to equilibrium ⋮ A dual skew symmetry for transient reflected Brownian motion in an orthant ⋮ Heavy-Traffic Insensitive Bounds for Weighted Proportionally Fair Bandwidth Sharing Policies

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• Naturality, standardness, and weak duality for Markov processes
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• Brownian motion in a wedge with oblique reflection
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