scholarly journals Change of drift in one-dimensional diffusions

2021 ◽  
Vol 25 (2) ◽  
pp. 359-381
Author(s):  
Sascha Desmettre ◽  
Gunther Leobacher ◽  
L. C. G. Rogers
Keyword(s):  
Heston Model ◽  
Local Martingale ◽  
Change Of Measure ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
Measure Change ◽  
Absence Of Arbitrage ◽  
Complete Characterisation

AbstractIt is generally understood that a given one-dimensional diffusion may be transformed by a Cameron–Martin–Girsanov measure change into another one-dimensional diffusion with the same volatility but a different drift. But to achieve this, we have to know that the change-of-measure local martingale that we write down is a true martingale. We provide a complete characterisation of when this happens. This enables us to discuss the absence of arbitrage in a generalised Heston model including the case where the Feller condition for the volatility process is violated.

scholarly journals Hopping and Flipping of RNA Polymerase on DNA during Recycling for Reinitiation after Intrinsic Termination in Bacterial Transcription

2021 ◽  
Vol 22 (5) ◽  
pp. 2398
Author(s):  
Wooyoung Kang ◽  
Seungha Hwang ◽  
Jin Young Kang ◽  
Changwon Kang ◽  
Sungchul Hohng
Keyword(s):  
Single Molecule ◽  
Transcription Initiation ◽  
Molecular Mechanisms ◽  
Facilitated Diffusion ◽  
One Dimensional ◽  
Bacterial Transcription ◽  
Fluorescence Measurements ◽  
Dimensional Diffusion ◽  
Single Molecule Studies ◽  
Hopping Diffusion

Two different molecular mechanisms, sliding and hopping, are employed by DNA-binding proteins for their one-dimensional facilitated diffusion on nonspecific DNA regions until reaching their specific target sequences. While it has been controversial whether RNA polymerases (RNAPs) use one-dimensional diffusion in targeting their promoters for transcription initiation, two recent single-molecule studies discovered that post-terminational RNAPs use one-dimensional diffusion for their reinitiation on the same DNA molecules. Escherichia coli RNAP, after synthesizing and releasing product RNA at intrinsic termination, mostly remains bound on DNA and diffuses in both forward and backward directions for recycling, which facilitates reinitiation on nearby promoters. However, it has remained unsolved which mechanism of one-dimensional diffusion is employed by recycling RNAP between termination and reinitiation. Single-molecule fluorescence measurements in this study reveal that post-terminational RNAPs undergo hopping diffusion during recycling on DNA, as their one-dimensional diffusion coefficients increase with rising salt concentrations. We additionally find that reinitiation can occur on promoters positioned in sense and antisense orientations with comparable efficiencies, so reinitiation efficiency depends primarily on distance rather than direction of recycling diffusion. This additional finding confirms that orientation change or flipping of RNAP with respect to DNA efficiently occurs as expected from hopping diffusion.

Effect of heterogeneity on the lag time in one‐dimensional diffusion

1988 ◽  
Vol 89 (4) ◽  
pp. 2278-2280 ◽  
Author(s):  
Jenn‐Shing Chen ◽  
Jeffrey L. Fox
Keyword(s):  
Lag Time ◽  
One Dimensional ◽  
Dimensional Diffusion
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