On Markov chain approximations for computing boundary crossing probabilities of diffusion processes

DOI10.1017/jpr.2023.11arXiv2112.05268OpenAlexW4376141724MaRDI QIDQ6148883

Konstantin A. Borovkov, Unnamed Author

Publication date: 12 January 2024

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

Full work available at URL: https://arxiv.org/abs/2112.05268

zbMATH Keywords

Markov chainsdiffusion processesboundary crossing probability

Mathematics Subject Classification ID

Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Diffusion processes (60J60) Numerical solutions to stochastic differential and integral equations (65C30)

Cites Work

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• Maximum-likelihood estimation for diffusion processes via closed-form density expansions
• First passage densities and boundary crossing probabilities for diffusion processes
• First exit time probability for multidimensional diffusions: A PDE-based approach
• Boundary crossing of Brownian motion. Its relation to the law of the iterated logarithm and to sequential analysis
• Normal approximation - some recent advances
• Double exponential formulas for numerical integration
• On the transformation of diffusion processes into the Wiener process
• On integral equations arising in the first-passage problem for Brownian motion
• Asymptotics of hitting probabilities for general one-dimensional pinned diffusions
• Weak approximation of killed diffusion using Euler schemes.
• Stopped diffusion processes: boundary corrections and overshoot
• Exact simulation of the first-passage time of diffusions
• First passage probabilities of one-dimensional diffusion processes
• Exact simulation of diffusions
• Crossing probabilities for diffusion processes with piecewise continuous boundaries
• Retrospective exact simulation of diffusion sample paths with applications
• A Continuity Correction for Discrete Barrier Options
• Boundary crossing probability for Brownian motion
• The probability distributions of the first hitting times of Bessel processes
• Linear and Nonlinear Boundary Crossing Probabilities for Brownian Motion and Related Processes
• Efficient Estimation of One-Dimensional Diffusion First Passage Time Densities via Monte Carlo Simulation
• A Modification of the Sequential Probability Ratio Test to Reduce the Sample Size
• A note on the evaluation of first-passage-time probability densities
• On an integral equation for first-passage-time probability densities
• On the two-boundary first-crossing-time problem for diffusion processes
• Smooth Transition Densities for One-Dimensional Diffusions
• Computations of boundary crossing probabilities for the wiener process
• A new integral equation for the evaluation of first-passage-time probability densities
• On the evaluation of first-passage-time probability densities via non-singular integral equations
• Brownian approximations to first passage probabilities
• Construction of first-passage-time densities for a diffusion process which is not necessarily time-homogeneous
• Evaluations of barrier-crossing probabilities of Wiener paths
• Boundary crossing probability for Brownian motion and general boundaries
• First-passage-time densities for time-non-homogeneous diffusion processes
• The distribution of brownian motion on linear stopping boundaries
• Practical Extrapolation Methods
• On evaluations and asymptotic approximations of first-passage-time probabilities
• Approximations of boundary crossing probabilities for a Brownian motion
• Exact simulation of first exit times for one-dimensional diffusion processes
• Explicit Bounds for Approximation Rates of Boundary Crossing Probabilities for the Wiener Process
• Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-form Approximation Approach
• Numerical Quadrature and Asymptotic Expansions
• The minimum of a stationary Markov process superimposed on a U-shaped trend
• On the Speed of Convergence in a Boundary Problem. II
• On the Speed of Convergence in a Boundary Problem. I
• On certain limit theorems of the theory of probability

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