Uniform convergence of conditional distributions for one-dimensional diffusion processes Article Swipe

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YOU? · · 2022 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2208.08911

In this paper, we study the quasi-stationary behavior of the one-dimensional diffusion process with a regular or exit boundary at 0 and an entrance boundary at $\infty$. By using the Doob's $h$-transform, we show that the conditional distribution of the process converges to its unique quasi-stationary distribution exponentially fast in the total variation norm, uniformly with respect to the initial distribution. Moreover, we also use the same method to show that the conditional distribution of the process converges exponentially fast in the $ψ$-norm to the unique quasi-stationary distribution. The rate of convergence of the conditional empirical measure to the quasi-ergodic distribution is also considered. Finally, two examples arising in population dynamics are also given to illustrate the main results.

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Mathematics Norm (philosophy) Distribution (mathematics) Conditional convergence Exponential distribution Diffusion process Stationary distribution Conditional probability distribution Boundary (topology) Convergence (economics) Exponential growth Diffusion Statistical physics Exponential function Mathematical analysis Stationary process Applied mathematics Statistics Physics Computer science Innovation diffusion Markov chain Economic growth Knowledge management Economics Political science Thermodynamics Law

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2208.08911
PDF: https://arxiv.org/pdf/2208.08911
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DOI: https://doi.org/10.48550/arxiv.2208.08911

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Title: Uniform convergence of conditional distributions for one-dimensional diffusion processes

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Language: en

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Publication year: 2022

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Publication date: 2022-08-18

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Authors: Guoman He, Hanjun Zhang

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Landing page: https://arxiv.org/abs/2208.08911

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Concepts: Mathematics, Norm (philosophy), Distribution (mathematics), Conditional convergence, Exponential distribution, Diffusion process, Stationary distribution, Conditional probability distribution, Boundary (topology), Convergence (economics), Exponential growth, Diffusion, Statistical physics, Exponential function, Mathematical analysis, Stationary process, Applied mathematics, Statistics, Physics, Computer science, Innovation diffusion, Markov chain, Economic growth, Knowledge management, Economics, Political science, Thermodynamics, Law

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institutions_distinct_count	2
sustainable_development_goals[0].id	https://metadata.un.org/sdg/10
sustainable_development_goals[0].score	0.47999998927116394
sustainable_development_goals[0].display_name	Reduced inequalities
citation_normalized_percentile