The Experts below are selected from a list of 138 Experts worldwide ranked by ideXlab platform
Jeremie Unterberger - One of the best experts on this subject based on the ideXlab platform.
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Moment estimates for solutions of linear stochastic differential equations driven by analytic fractional Brownian motion
Electronic Communications in Probability, 2010Co-Authors: Jeremie UnterbergerAbstract:As a general rule, differential equations driven by a multi-dimensional Irregular Path $\Gamma$ are solved by constructing a rough Path over $\Gamma$. The domain of definition - and also estimates - of the solutions depend on upper bounds for the rough Path; these general, deterministic estimates are too crude to apply e.g. to the solutions of stochastic differential equations with linear coefficients driven by a Gaussian process with Holder regularity $\alpha
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Moment estimates for solutions of linear stochastic differential equations driven by analytic fractional Brownian motion
arXiv: Probability, 2009Co-Authors: Jeremie UnterbergerAbstract:As a general rule, differential equations driven by a multi-dimensional Irregular Path $\Gamma$ are solved by constructing a rough Path over $\Gamma$. The domain of definition ? and also estimates ? of the solutions depend on upper bounds for the rough Path; these general, deterministic estimates are too crude to apply e.g. to the solutions of stochastic differential equations with linear coefficients driven by a Gaussian process with H\"older regularity $\alpha < 1/2$. We prove here (by showing convergence of Chen's series) that linear stochastic differential equations driven by analytic fractional Brownian motion [7, 8] with arbitrary Hurst index $\alpha \in (0, 1)$ may be solved on the closed upper halfplane, and that the solutions have finite variance.
Paul Krühner - One of the best experts on this subject based on the ideXlab platform.
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Hölder continuous densities of solutions of SDEs with measurable and Path dependent drift coefficients
Stochastic Processes and their Applications, 2017Co-Authors: David Baños, Paul KrühnerAbstract:We consider a process given as the solution of a one-dimensional stochastic differential equation with Irregular, Path dependent and time-inhomogeneous drift coefficient and additive noise. Holder continuity of the density at any given time is achieved using a different approach than the classical ones in the literature. Namely, the Holder regularity is obtained via a control problem by identifying the equation with the worst global Holder constant. Then we generalise our findings to a larger class of diffusions. The novelty of this method is that it is not based on a variational calculus and it is suitable for non-Markovian processes.
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H\"older continuous densities of solutions of SDEs with measurable and Path dependent drift coefficients
arXiv: Probability, 2016Co-Authors: David Baños, Paul KrühnerAbstract:We consider a process given as the solution of a one-dimensional stochastic differential equation with Irregular, Path dependent and time-inhomogeneous drift coefficient and additive noise. H\"older continuity of the Lebesgue density of that process at any given time is achieved using a different approach than the classical ones in the literature. Namely, the H\"older regularity of the densities is obtained via a control problem by identifying the stochastic differential equation with the worst global H\"older constant. Then we generalise our findings to a larger class of diffusion coefficients. The novelty of this method is that it is not based on a variational calculus and it is suitable for non-Markovian processes.
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Optimal bounds for the densities of solutions of SDEs with measurable and Path dependent drift coefficients
arXiv: Probability, 2014Co-Authors: David Baños, Paul KrühnerAbstract:We consider a process given as the solution of a stochastic differential equation with Irregular, Path dependent and time-inhomogeneous drift coefficient and additive noise. Explicit and optimal bounds for the Lebesgue density of that process at any given time are derived. The bounds and their optimality is shown by identifying the worst case stochastic differential equation. Then we generalise our findings to a larger class of diffusion coefficients.
David Baños - One of the best experts on this subject based on the ideXlab platform.
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Hölder continuous densities of solutions of SDEs with measurable and Path dependent drift coefficients
Stochastic Processes and their Applications, 2017Co-Authors: David Baños, Paul KrühnerAbstract:We consider a process given as the solution of a one-dimensional stochastic differential equation with Irregular, Path dependent and time-inhomogeneous drift coefficient and additive noise. Holder continuity of the density at any given time is achieved using a different approach than the classical ones in the literature. Namely, the Holder regularity is obtained via a control problem by identifying the equation with the worst global Holder constant. Then we generalise our findings to a larger class of diffusions. The novelty of this method is that it is not based on a variational calculus and it is suitable for non-Markovian processes.
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H\"older continuous densities of solutions of SDEs with measurable and Path dependent drift coefficients
arXiv: Probability, 2016Co-Authors: David Baños, Paul KrühnerAbstract:We consider a process given as the solution of a one-dimensional stochastic differential equation with Irregular, Path dependent and time-inhomogeneous drift coefficient and additive noise. H\"older continuity of the Lebesgue density of that process at any given time is achieved using a different approach than the classical ones in the literature. Namely, the H\"older regularity of the densities is obtained via a control problem by identifying the stochastic differential equation with the worst global H\"older constant. Then we generalise our findings to a larger class of diffusion coefficients. The novelty of this method is that it is not based on a variational calculus and it is suitable for non-Markovian processes.
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Optimal bounds for the densities of solutions of SDEs with measurable and Path dependent drift coefficients
arXiv: Probability, 2014Co-Authors: David Baños, Paul KrühnerAbstract:We consider a process given as the solution of a stochastic differential equation with Irregular, Path dependent and time-inhomogeneous drift coefficient and additive noise. Explicit and optimal bounds for the Lebesgue density of that process at any given time are derived. The bounds and their optimality is shown by identifying the worst case stochastic differential equation. Then we generalise our findings to a larger class of diffusion coefficients.
P. E. J. Flewitt - One of the best experts on this subject based on the ideXlab platform.
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The formation of fracture process zones in polygranular graphite as a precursor to fracture
Journal of Materials Science, 2013Co-Authors: Soheil Nakhodchi, David J. Smith, P. E. J. FlewittAbstract:The initiation and growth of fracture process zones are explored in polygranular Pile Grade A reactor core moderator graphite subjected to four-point bending. Digital image correlation is combined with resistance strain gauge measurements to evaluate both the localised and the global strains during tests on graphite. The experiments, performed on plain and notched rectangular beam specimens, show non-linear load–displacement characteristics prior to peak load. This behaviour is shown to be mainly dominated by the presence of localised strains (or process zones) extending up to about 3 mm from the tensile surface of the specimen. At peak load, a macrocrack propagates rapidly along an Irregular Path controlled by the direction of the applied load and the microstructure of the graphite. These cracks arrest prior to complete separation of the specimen. Once cracks are formed, localised tensile displacements extend for distances of up to about 3 mm ahead of the tips of these cracks. It is also demonstrated that failure load is not sensitive to the presence of the notch. The results are discussed with respect to the role of process zones on the non-linear load–displacement response of the graphite prior to the peak load and during macrocrack propagation post peak load.
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Crack initiation and propagation in pile grade A (PGA) reactor core graphite under a range of loading conditions
Journal of Nuclear Materials, 2010Co-Authors: Peter J Heard, R Moskovic, M.r. Wootton, P. E. J. FlewittAbstract:Abstract The pile grade A (PGA) graphite used in UK gas cooled reactors is a multiphase, polygranular, aggregate material with complex cracking behaviour. Virgin, un-irradiated graphite cylinders 12 mm in diameter and 6 mm long have been subjected to controlled cracking either by insertion of a needle into the material or by compressive loading. The resultant cracking was observed using optical and focused ion beam microscopy. Micro-cracking was confirmed to precede macro-crack formation and this mechanism is consistent with the observed non-linearity in the load–displacement curve prior to peak load. Macro-cracks followed an Irregular Path controlled by the direction of the applied tensile stress and the microstructure, in particular porosity and filler particles. The results are discussed with respect to the quasi-brittle fracture characteristics of such an aggregate material.
Soheil Nakhodchi - One of the best experts on this subject based on the ideXlab platform.
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The formation of fracture process zones in polygranular graphite as a precursor to fracture
Journal of Materials Science, 2013Co-Authors: Soheil Nakhodchi, David J. Smith, P. E. J. FlewittAbstract:The initiation and growth of fracture process zones are explored in polygranular Pile Grade A reactor core moderator graphite subjected to four-point bending. Digital image correlation is combined with resistance strain gauge measurements to evaluate both the localised and the global strains during tests on graphite. The experiments, performed on plain and notched rectangular beam specimens, show non-linear load–displacement characteristics prior to peak load. This behaviour is shown to be mainly dominated by the presence of localised strains (or process zones) extending up to about 3 mm from the tensile surface of the specimen. At peak load, a macrocrack propagates rapidly along an Irregular Path controlled by the direction of the applied load and the microstructure of the graphite. These cracks arrest prior to complete separation of the specimen. Once cracks are formed, localised tensile displacements extend for distances of up to about 3 mm ahead of the tips of these cracks. It is also demonstrated that failure load is not sensitive to the presence of the notch. The results are discussed with respect to the role of process zones on the non-linear load–displacement response of the graphite prior to the peak load and during macrocrack propagation post peak load.
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Fracture Process Zones in Polygranular Graphite in Bending
Key Engineering Materials, 2010Co-Authors: Soheil Nakhodchi, A Hodgkins, R Moskovic, David J. Smith, Peter E J FlewittAbstract:The formation of fracture process zones in polygranular reactor core moderator graphites subjected to four-point bending has been investigated. The three-dimensional digital image correlation technique has been combined with resistance strain gauge measurements to evaluate, both the localised and the global displacements during testing. The non-linear load-displacement characteristics prior to peak load are correlated with the localised displacements which can extend up to ~3mm (process zone) from the tensile surface of the specimen. At peak load a macro-crack propagates rapidly along an Irregular Path controlled by the direction of the applied tensile load and the microstructure of the graphite. These cracks arrest prior to complete separation of the specimen. Localised tensile process zones extend for distances of up to ~3mm ahead of the tips of these cracks.
