Exit times of Brownian motion, harmonic majorization, and Hardy spaces

DOI10.1016/0001-8708(77)90029-9zbMath0372.60112OpenAlexW1990295631MaRDI QIDQ1243992

Publication date: 1977

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0001-8708(77)90029-9

Mathematics Subject Classification ID

Brownian motion (60J65) Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Stopping times; optimal stopping problems; gambling theory (60G40) Connections of harmonic functions with differential equations in two dimensions (31A35)

Related Items

The first exit time of planar Brownian motion from the interior of a parabola ⋮ On the exact constants in one-sided maximal inequalities for Bessel processes ⋮ Iterated Brownian motion in an open set. ⋮ Higher order PDEs and symmetric stable processes ⋮ Iterated Brownian motion in bounded domains in \(\mathbb {R}^n\) ⋮ On the asymptotic behavior of the occupation time in cones of \(d\)-dimensional Brownian motion ⋮ Symmetric stable processes on unbounded domains ⋮ Symmetric stable processes in parabola–shaped regions ⋮ Weak Subordination and Stable Classes of Meromorphic Functions ⋮ A representation of local time for Lipschitz surfaces ⋮ Longtime Behavior for Mutually Catalytic Branching with Negative Correlations ⋮ Upper bounds for the \(L_ p\)-norms of martingales ⋮ Remarks on Gross' technique for obtaining a conformal Skorohod embedding of planar Brownian motion ⋮ Brownian motion in a quasi-cone ⋮ The first exit time of a Brownian motion from an unbounded convex domain ⋮ Infinite rate mutually catalytic branching in infinitely many colonies: construction, characterization and convergence ⋮ Steady-state simulation of reflected Brownian motion and related stochastic networks ⋮ Estimates for inverse coefficients of univalent functions from integral means ⋮ The expected time to end the tug-of-war in a wedge ⋮ One-sided maximal inequalities for a randomly stopped Bessel process ⋮ A collection of results relating the geometry of plane domains and the exit time of planar Brownian motion ⋮ Integrability properties and limit theorems for the exit time from a cone of planar Brownian motion ⋮ Non-extinction of a Fleming-Viot particle model ⋮ A new solution to the conformal Skorokhod embedding problem and applications to the Dirichlet eigenvalue problem ⋮ On the probability of fast exits and long stays of a planar Brownian motion in simply connected domains ⋮ The exit time of planar Brownian motion and the Phragmén-Lindelöf principle ⋮ BOUNDS FOR EXPONENTIAL MOMENTS OF BESSEL PROCESSES ⋮ Radial rearrangement, harmonic measures and extensions of Beurling's shove theorem ⋮ Extremal geometry of a Brownian porous medium ⋮ Brownian Motion with Partial Information ⋮ Properties of extremal functions for some nonlinear functionals on Dirichlet spaces ⋮ Maximizing the pth moment of the exit time of planar brownian motion from a given domain ⋮ Brownian motion with a horizontal Bessel drift in a parabolic-type domain ⋮ Reflected Brownian Motion in a Cone with Radially Homogeneous Reflection Field ⋮ Exit times of N-dimensional random walks ⋮ The Martin kernel for unbounded domains ⋮ Exit problems associated with finite reflection groups ⋮ Sharp integrability for Brownian motion in parabola-shaped regions ⋮ Moments of the Lifetime of Conditioned Brownian Motion in Cones ⋮ L p estimates for stopping times of Bessel processes ⋮ Infinite rate mutually catalytic branching ⋮ Asymptotic behavior of positive harmonic functions in certain unbounded domains ⋮ A Conformal Inequality Related to the Conditional Gauge Theorem ⋮ On the finiteness of moments of the exit time of planar Brownian motion from comb domains ⋮ Moments of exit times from wedges for non-homogeneous random walks with asymptotically zero drifts ⋮ On the occupation times of cones by Brownian motion ⋮ Analytic-geometric methods for finite Markov chains with applications to quasi-stationarity ⋮ Some improvements on the L_p inequalities for diffusion processes ⋮ On the Hardy number of comb domains ⋮ A method for deriving hypergeometric and related identities from theH²Hardy norm of conformal maps ⋮ Conformal Skorokhod embeddings and related extremal problems ⋮ Strong differential subordination and sharp inequalities for orthogonal processes ⋮ AN INTEGRAL EQUATION FOR THE DISTRIBUTION OF THE FIRST EXIT TIME OF A REFLECTED BROWNIAN MOTION ⋮ The exit distribution for iterated Brownian motion in cones ⋮ A value-distribution criterion for the class L log L, and some related questions ⋮ The range of Hardy numbers for comb domains ⋮ Windings of Planar Stable Processes ⋮ On the duration of stays of Brownian motion in domains in Euclidean space ⋮ Martin kernel for fractional Laplacian in narrow cones ⋮ Barriers, exit time and survival probability for unimodal Lévy processes ⋮ Random walks in cones ⋮ Exit times from cones in \({\mathbb{R}}^ n\) of Brownian motion ⋮ Spectral upper bound for the torsion function of symmetric stable processes ⋮ The lifetime of conditioned Brownian motion in certain Lipschitz domains

Cites Work