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Olivier Menoukeu-Pamen Thilo Meyer-Brandis Torstein Nilssen Frank Proske Tusheng Zhang 《Mathematische Annalen》2013,357(2):761-799
In this article we develop a new approach to construct solutions of stochastic equations with merely measurable drift coefficients. We aim at demonstrating the principles of our technique by analyzing strong solutions of stochastic differential equations driven by Brownian motion. An important and rather surprising consequence of our method which is based on Malliavin calculus is that the solutions derived by Veretennikov (Theory Probab Appl 24:354–366, 1979) for Brownian motion with bounded and measurable drift in $\mathbb{R }^{d}$ are Malliavin differentiable. Further, a strength of our approach, which does not rely on a pathwise uniqueness argument, is that it can be transferred and applied to the analysis of various other types of (stochastic) equations: We obtain a Bismut–Elworthy–Li formula (Elworthy and Li, J Funct Anal 125:252–286, 1994) for spatial derivatives of solutions to the Kolmogorov equation with bounded and measurable drift coefficients. To derive the formula, we use that our approach can be applied to obtain Sobolev differentiability in the initial condition in addition to Malliavin differentiability of the associated stochastic differential equations. Another application of our technique is the construction of unique solutions of the stochastic transport equation with irregular vector fields. Moreover, our approach is also applicable to the construction of solutions of stochastic evolution equations on Hilbert spaces. 相似文献
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H. Mühe Mc. Candless E. Valenta Utz Wilh Vaubel B. Ahlström O. Aschan J. Kondakow J. Schindelmeiser R. Böhme H. Herzfeld J. E. Teeple R. Adan J. Marcusson Darmois H. Wolff C. Piest R. Marcille EA. Parry M. Adams H. W. Fosse K. Ihnatowzcz 《Analytical and bioanalytical chemistry》1917,56(10-11):541-560
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Torstein Nilssen 《Stochastics An International Journal of Probability and Stochastic Processes》2016,88(5):779-802
In this paper we develop a method for constructing strong solutions of one-dimensional Stochastic Differential Equations where the drift may be discontinuous and unbounded. The driving noise is the Brownian Motion and we show that the solution is Sobolev-differentiable in the initial condition and Malliavin differentiable. This method is not based on a pathwise uniqueness argument. We will apply these results to the stochastic transport equation. More specifically, we obtain a continuously differentiable solution of the stochastic transport equation when the driving function is a step function. 相似文献
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RD Harris WS Baker Van Stipdonk MJ RM Crooks EA Schweikert 《Rapid communications in mass spectrometry : RCM》1999,13(14):1374-1380
A suite of keV polyatomic or 'cluster' projectiles was used to bombard unoxidized and oxidized self-assembled monolayer surfaces. Negative secondary ion yields, collected at the limit of single ion impacts, were measured and compared for both molecular and fragment ions. In contrast to targets that are orders of magnitude thicker than the penetration range of the primary ions, secondary ion yields from polyatomic projectile impacts on self-assembled monolayers show little to no enhancement when compared with monatomic projectiles at the same velocity. This unusual trend is most likely due to the structural arrangement and bonding characteristics of the monolayer molecules with the Au(111). Copyright 1999 John Wiley & Sons, Ltd. 相似文献
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Aderholz M Aggarwal MM Akbari H Allport PP Badyal SK Ballagh HC Barth M Baton JP Bingham HH Brucker EB Burnstein RA Campbell JR Cence RJ Chatterjee TK Clayton EF Corrigan G Coutures C DeProspo D Devanand De Wolf EA Faulkner PJ Foeth H Fretter WB Gupta VK Hanlon J Harigel G Harris FA Jabiol MA Jacques P Jain V Jones GT Jones MD Kafka T Kalelkar M Kasper P Kohli JM Koller EL Krawiec RJ Lauko M Lys JE Marage P Milburn RH Miller DB Mittra IS Mobayyen MM Moreels J Morrison DR Myatt G Nailor P 《Physical review D: Particles and fields》1992,45(7):2232-2243
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