Limit at Zero of the First-Passage Time Density and the Inverse Problem for One-Dimensional Diffusions

DOI10.1080/07362990600958804zbMath1116.60041OpenAlexW2155006152MaRDI QIDQ3423709

Mario Abundo

Publication date: 15 February 2007

Published in: Stochastic Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/07362990600958804

zbMATH Keywords

stochastic differential equationBrownian motionmoving boundaryfirst-passage timeFeller diffusioninverse first-passage time problemfirst-passage time problem

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stopping times; optimal stopping problems; gambling theory (60G40) Diffusion processes (60J60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35)

Related Items (14)

The randomized first-hitting problem of continuously time-changed Brownian motion ⋮ One-Dimensional Reflected Diffusions with Two Boundaries and an Inverse First-Hitting Problem ⋮ Higher-Order Regularity of the Free Boundary in the Inverse First-Passage Problem ⋮ On mimicry among sequential sampling models ⋮ 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 ⋮ The mean of the running maximum of an integrated Gauss–Markov process and the connection with its first-passage time ⋮ An inverse first-passage problem for one-dimensional diffusions with random starting point ⋮ An approximation for the inverse first passage time problem ⋮ On the first hitting time of a one-dimensional diffusion and a compound Poisson process ⋮ A randomized first-passage problem for drifted Brownian motion subject to hold and jump from a boundary ⋮ First-Passage Problems for One-Dimensional Diffusions with Random Jumps from a Boundary ⋮ Solving an Inverse First-Passage-Time Problem for Wiener Process Subject to Random Jumps from a Boundary ⋮ First-Passage Problems for Asymmetric Diffusions and Skew-diffusion Processes

Cites Work

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• On the transformation of diffusion processes into the Wiener process
• Limit at zero of the Brownian first-passage density
• Some conditional crossing results of Brownian motion over a piecewise-linear boundary
• On the first hitting time and the last exit time for a Brownian motion to/from a moving boundary
• Martingales, Tauberian Theorem, and Strategies of Gambling
• On explicit solutions to stochastic differential equations
• On the First-Passage Time of a Diffusion Process Over a One-Sided Stochastic Boundary
• On first–crossing times of one–dimensional diffusions over two time–dependent boundaries
• The minimum of a stationary Markov process superimposed on a U-shaped trend
• Boundary-crossing probabilities for the Brownian motion and Poisson processes and techniques for computing the power of the Kolmogorov-Smirnov test
• On the inverse of the first passage time probability problem
• Asymptotics of first-passage time over a one-sided stochastic boundary

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