Brownian motion conditioned to spend limited time below a barrier

Аурзада, Франк; Schickentanz, Dominic T.

doi:10.1016/j.spa.2022.01.007

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Brownian Bridge Estimates2

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Cited by 2 publications

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“…1 ) Then The conditional probability in ( 4.6 ) is known (Pechtl 1999 , 2020 ). A more convenient formula is given in Aurzada and Schickentanz ( 2022 ), see Eq. (7) therein.…”

Section: Brownian Bridge Estimatesmentioning

confidence: 99%

The speed of invasion in an advancing population

Bovier,

Hartung

2023

J. Math. Biol.

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We derive rigorous estimates on the speed of invasion of an advantageous trait in a spatially advancing population in the context of a system of one-dimensional F-KPP equations. The model was introduced and studied heuristically and numerically in a paper by Venegas-Ortiz et al. (Genetics 196:497–507, 2014). In that paper, it was noted that the speed of invasion by the mutant trait is faster when the resident population is expanding in space compared to the speed when the resident population is already present everywhere. We use the Feynman–Kac representation to provide rigorous estimates that confirm these predictions.

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“…1 ) Then The conditional probability in ( 4.6 ) is known (Pechtl 1999 , 2020 ). A more convenient formula is given in Aurzada and Schickentanz ( 2022 ), see Eq. (7) therein.…”

Section: Brownian Bridge Estimatesmentioning

confidence: 99%

The speed of invasion in an advancing population

Bovier,

Hartung

2023

J. Math. Biol.

View full text Add to dashboard Cite

show abstract

“…The conditional probability in (4.6) is known [19,18]. A more convenient formula is given in [2], see Eq. ( 7) therein.…”

Section: Brownian Bridge Estimatesmentioning

confidence: 99%

The speed of invasion in an advancing population

Bovier¹,

Hartung²

2022

Preprint

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We derive rigorous estimates on the speed of invasion of an advantageous trait in a spatially advancing population in the context of a system of one-dimensional F-KPP equations. The model was introduced and studied heuristically and numerically in a paper by . In that paper, it was noted that the speed of invasion by the mutant trait is faster faster when the resident population ist expanding in space compared to the speed when the resident population is already present everywhere. We use the Feynman-Kac representation to provide rigorous estimates that confirm these predictions.

show abstract

Brownian motion conditioned to spend limited time below a barrier

Cited by 2 publications

References 22 publications

The speed of invasion in an advancing population

The speed of invasion in an advancing population

The speed of invasion in an advancing population

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