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The Range of Stochastic Integration
The Annals of Probability, 1978 Every measurable real-valued function $f$ on the space of Wiener process paths with $E(|f|^p) < \infty$ (where $0 < p < 1$) can be represented as a stochastic integral $f = \int \varphi dX$, where $E(\int \varphi^2(t)dt)^{p/2} < \infty$. A similar result holds for $1 < p < \infty$ if and only if $E(f) = 0$.
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Efficient discretization of stochastic integrals [PDF]
Finance and Stochastics, 2013 Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves seemingly new. Asymptotically efficient schemes which attain the lower bounds are constructed explicitly.
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Ligand‐dependent transcriptional heterogeneity in cell cycle gene expression delays G1/S entry
FEBS Letters, EarlyView.EGF and HRG induce distinct G1/S progression programs in ErbB2‐amplified BT474 breast cancer cells. Despite activating the potent ErbB2–ErbB3 heterodimer, HRG does not accelerate cell‐cycle entry. Instead, EGF promotes earlier restriction‐point passage via ERK–FOS signaling, whereas HRG activates the AKT–MYC axis, driving transcriptional heterogeneity ...
Ririn Rahmala Febri +5 more
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Journal of Inequalities and Applications, 2023 In this investigation, we unfold the Jensen–Mercer ( J − M $\mathtt{J-M}$ ) inequality for convex stochastic processes via a new fractional integral operator.
Fahd Jarad +5 more
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Synergistic perspectives—How single‐molecule biophysics complement biochemical understanding
FEBS Letters, EarlyView.In this review, we discuss how ensemble biochemistry and single‐molecule approaches are complementary, outline commonly used single‐molecule techniques, and illustrate their relevance through two representative case studies: chromatin organization by SMC complexes and pathway choice during DNA double‐strand break repair.
Sara De Bragança +2 more
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A Comparison of Stochastic Integrals
The Annals of Probability, 1979 the existence of the star integral, we give a formula relating the two integrals. We show that the star integral is equal to the dot integral provided one takes a projection of the integrand onto the space of predictable processes before evaluating the dot integral.
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Stochastic dynamic equations on general time scales
Electronic Journal of Differential Equations, 2013 In this article, we construct stochastic integral and stochastic differential equations on general time scales. We call these equations stochastic dynamic equations.
Martin Bohner +2 more
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Numerical solution of nonlinear stochastic Itô–Volterra integral equations based on Haar wavelets
Advances in Difference Equations, 2019 In this paper, an efficient numerical method is presented for solving nonlinear stochastic Itô–Volterra integral equations based on Haar wavelets.
Jieheng Wu, Guo Jiang, Xiaoyan Sang
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Karpatsʹkì Matematičnì Publìkacìï, 2014 The operators of stochastic differentiation, which are closely related with the extended Skorohod stochastic integral and with the Hida stochastic derivative, play an important role in the classical (Gaussian) white noise analysis.
M.M. Dyriv, N.A. Kachanovsky
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Membrane composition and thermodynamic identity as boundaries of life for synthetic cell research
FEBS Letters, EarlyView.What makes a cell a cell? The boundary of a living cell is not just a wall. Read as a Markov blanket, the membrane separates internal from external states, generating identity and non‐equilibrium order. Can this identity be rebuilt from scratch in a synthetic cell?
Caterina Presutti, Bert Poolman
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