Representation of self-similar Gaussian processes

We develop the canonical Volterra representation for a self-similar Gaussian process by using the Lamperti transformation of the corresponding stationary Gaussian process, where this latter one admits a canonical integral representation under the assumption of pure non-determinism. We apply the representation obtained for the self-similar Gaussian process to derive an expression for Gaussian processes that are equivalent in law to the self-similar Gaussian process in question

Necessary and Sufficient Conditions for H\"older Continuity of Gaussian Processes

The continuity of Gaussian processes is extensively studied topic and it culminates in the Talagrand's notion of majorizing measures that gives complicated necessary and sufficient conditions. In this note we study the H\"older continuity of Gaussian processes. It turns out that necessary and sufficient conditions can be stated in a simple form that is a variant of the celebrated Kolmogorov-\v{C}entsov condition

Representations and regularity of Gaussian processes

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Synthetic considerations in the self-assembly of coordination polymers of pyridine-functionalised hybrid Mn-Anderson polyoxometalates

The incorporation of polyoxometalates (POMs) as structural units into ordered porous constructs such as metal-organic frameworks (MOFs) is desirable for a range of applications where intrinsic properties inherited from both the MOF and POM are utilised, including catalysis and magnetic data storage. The controlled self-assembly of targeted MOF topologies containing POM units is hampered by the wide range of oxo and hydroxo units on the peripheries of POMs that can act as coordinating groups towards linking metal cations leading to a diverse range of structures, but incorporation of organic donor units into hybrid POMs offers an alternative methodology to programmably synthesise POM/MOF conjugates. Herein, we report six coordination polymers obtained serendipitously wherein Zn2+ and Cu2+ link pyridine-appended Mn-Anderson clusters into two- and three-dimensional network solids with complex connectivities and topologies. Careful inspection of their solid-state structures has allowed us to identify common structure-directing features across these coordination polymers, including a square motif where two Zn2+ cations bridge two POMs. By correlating certain structural motifs with synthetic conditions we have formulated a series of design considerations for the self-assembly of coordination polymers of hybrid POMs, encompassing the selection of reaction conditions, co-ligands and linking metal cations. We anticipate that these synthetic guidelines will inform the future assembly of hybrid POMs into functional MOF materials

One pot solvothermal synthesis of organic acid coated magnetic iron oxide nanoparticles

Indexación: ScieloABSTRACT In this work we present the synthesis and characterization of iron oxide nanoparticles (IONPs), which were structurally and magnetically characterized. The use of iron salts and an organic acid (l-serine or ascorbic acid) as precursors under solvothermal conditions yielded these coated IONPs. The powder X-ray diffraction pattern of FeO-1 and FeO-2 is consistent with hematite (α-Fe2O3) and hematite-maghemite ((α-Fe2O3/γ-Fe2O3) respectively. The TEM analysis permits to estimate an average size of 10 nm for the FeO-1 sample. The magnetic characterization of the samples through the M(H) plots showed a very low coercivity value for both samples, being 53 Oe for FeO-1 and 10 Oe for FeO-2, indicating the very weak ferromagnetic character of the synthesized iron oxide species. Even though both organic acids under solvothermal conditions permit to obtain coated IONPs in one pot reaction, l-serine produces a more narrow-size distribution

Virtual devices as a service

Software applications are developed and tested over a large and evolving variety of devices of different device types. Development and testing with physical devices is tedious and time consuming and has scaling and reliability problems. Per techniques of this disclosure, a large pool of virtual devices is instantiated on a compute cluster and made available to software developers as a service. Developers check out as many virtual devices as needed, conduct test and development activity, reset the devices, and release the devices back to the pool. The techniques obviate the need for physical devices and the concomitant issues of cost and reliability and enable large scale testing and development and faster device releases

Generalized Gaussian Bridges

A generalized bridge is the law of a stochastic process that is conditioned on N linear functionals of its path. We consider two types of representations of such bridges: orthogonal and canonical. The orthogonal representation is constructed from the entire path of the underlying process. Thus, future knowledge of the path is needed. The orthogonal representation is provided for any continuous Gaussian process. In the canonical representation the filtrations and the linear spaces generated by the bridge process and the underlying process coincide. Thus, no future information of the underlying process is needed. Also, in the semimartingale case the canonical bridge representation is related to the enlargement of filtration and semimartingale decompositions. The canonical representation is provided for the so-called prediction-invertible Gaussian processes. All martingales are trivially prediction-invertible. A typical non-semimartingale example of a prediction-invertible Gaussian process is the fractional Brownian motion. We apply the canonical bridges to insider trading

On the conditional small ball property of multivariate Lévy-driven moving average processes

We study whether a multivariate Lévy-driven moving average process can shadow arbitrarily closely any continuous path, starting from the present value of the process, with positive conditional probability, which we call the conditional small ball property. Our main results establish the conditional small ball property for Lévy-driven moving average processes under natural non-degeneracy conditions on the kernel function of the process and on the driving Lévy process. We discuss in depth how to verify these conditions in practice. As concrete examples, to which our results apply, we consider fractional Lévy processes and multivariate Lévy-driven Ornstein–Uhlenbeck processes