2019
DOI: 10.1080/07362994.2019.1694416
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Properties of bounded stochastic processes employed in biophysics

Abstract: Properties of bounded stochastic processes employed in biophysics. Stochastic Analysis and Applications, 38 (2). pp. 277-306.

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Cited by 19 publications
(14 citation statements)
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“…In this case the link function ζ(y) is simply ζ(y) = By An instance of this class of noises is the Doering-Cai-Lin noise, introduced in [69,70] and whose properties where studied in [71] where…”
Section: 'Recipes' To Model Bounded Noisesmentioning
confidence: 99%
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“…In this case the link function ζ(y) is simply ζ(y) = By An instance of this class of noises is the Doering-Cai-Lin noise, introduced in [69,70] and whose properties where studied in [71] where…”
Section: 'Recipes' To Model Bounded Noisesmentioning
confidence: 99%
“…Note that in in [71] it was shown that if δ = −1/2 then the DCL noise is equal in law to the well-known and widely adopted sine-Wiener noise, introduced in [72], and defined by setting k(y) = 0 and z(y) = Bsin(y).…”
Section: 'Recipes' To Model Bounded Noisesmentioning
confidence: 99%
“…In the above, we used the estimate E [X t − X k ] ≤ f (t − kδ) ≤ f (t ∧ t − kδ) taking into account that {X t∧ t} t is a martingale and so the respective Itō integral vanishes in the said estimate after applying the expected value operator. Using (22), we may bound δ so as to yield:…”
Section: Main Theoremmentioning
confidence: 99%
“…Another way to tackle the discussed issue is to consider noise models different to the Brownian motion, specifically, bounded ones, i. e., those whose realizations are bounded a. s.. Such models are known, and for a good review, the reader may refer to [22]. We briefly mention these for the sake of completeness.…”
Section: Generalizations and Applicationsmentioning
confidence: 99%
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