Existence and uniqueness of solutions to the inverse boundary crossing problem for diffusions

DOI10.1214/10-AAP714zbMath1244.60078arXiv1112.5305OpenAlexW2052010760MaRDI QIDQ655577

Xinfu Chen, David Saunders, Lan Cheng, John M. Chadam

Publication date: 4 January 2012

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1112.5305

zbMATH Keywords

variational inequalitiesBrownian motiondiffusion processesviscosity solutionsinverse boundary crossing problem

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Diffusion processes (60J60) Sample path properties (60G17) Free boundary problems for PDEs (35R35)

Related Items (12)

Uniqueness of the Inverse First-Passage Time Problem and the Shape of the Shiryaev Boundary ⋮ Geometry of distribution-constrained optimal stopping problems ⋮ The gamma renewal process as an output of the diffusion leaky integrate-and-fire neuronal model ⋮ The inverse first passage time problem for killed Brownian motion ⋮ Efficient discretisation of stochastic differential equations ⋮ Linear programming fictitious play algorithm for mean field games with optimal stopping and absorption ⋮ Higher-Order Regularity of the Free Boundary in the Inverse First-Passage Problem ⋮ The inverse first-passage time problem as hydrodynamic limit of a particle system ⋮ An elementary approach to the inverse first-passage-time problem for soft-killed Brownian motion ⋮ Killed Brownian motion with a prescribed lifetime distribution and models of default ⋮ The inverse first passage time method for a two dimensional Ornstein Uhlenbeck process with neuronal application ⋮ Explicit solution of an inverse first-passage time problem for Lévy processes and counterparty credit risk

Cites Work

• On the inverse first-passage-time problem for a Wiener process
• On integral equations arising in the first-passage problem for Brownian motion
• Analysis of an Inverse First Passage Problem from Risk Management
• On Markov Stopping Times with a Given Distribution for a Wiener Process
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