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Subordinator

About: Subordinator is a research topic. Over the lifetime, 771 publications have been published within this topic receiving 15383 citations.


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TL;DR: In this article, a subordinated Langevin process, with a random operational time in the form of an inverse strictly increasing Levy-type subordinator, is considered as a generalization of the conventional perfect and leaky integrate-and-fire neuron models.
Abstract: A subordinated Langevin process, with a random operational time in the form of an inverse strictly increasing Levy-type subordinator, is considered as a generalization of the conventional perfect and leaky integrate-and-fire neuron models. The parent process is given by standard Brownian motion. The effect of the random activity of synaptic inputs, which arises from other neurons forming local and distant networks, is modeled via a Levy exponent of the subordinator. Using a first-passage-time formulation in an external force field, we find exact expressions for the Laplace transform of the output interspike interval (ISI) density. More detailed analysis is presented on the properties of the ISI distribution in the case of the Levy exponent which corresponds to the truncated double-order time-fractional diffusion equation for the probability density of the membrane potential. Particularly, it is shown that at some parameter regimes the ISI density exhibits a bimodal structure. Moreover, it is demonstrated that the ISIs regularity is maximized at an intermediate value of the mean input current.

3 citations

Journal ArticleDOI
TL;DR: It is shown that at some parameter regimes the ISI density exhibits a multimodal structure and it is demonstrated that the coefficient of variation, the serial correlation coefficient, and the Fano factor display a nonmonotonic dependence on the mean input current μ.
Abstract: The behavior of a stochastic perfect integrate-and-fire (PIF) model of neurons is considered. The effect of temporally correlated random activity of synaptic inputs is modeled as a combination of an asymmetric dichotomous noise and a random operation time in the form of an inverse strictly increasing Levy-type subordinator. Using a first-passage-time formulation, we find exact expressions for the output interspike interval (ISI) statistics. Particularly, it is shown that at some parameter regimes the ISI density exhibits a multimodal structure. Moreover, it is demonstrated that the coefficient of variation, the serial correlation coefficient, and the Fano factor display a nonmonotonic dependence on the mean input current μ, i.e., the ISI's regularity is maximized at an intermediate value of μ. The features of spike statistics, analytically revealed in our study, are compared with previously obtained results for a perfect integrate-and-fire neuron model driven by dichotomous noise (without subordination).

3 citations

Journal ArticleDOI
01 May 2020
TL;DR: In this article, the compound Poisson processes of order $k$ (CPPoK) were introduced and its properties were discussed, using mixture of tempered stable subordinator and its right continuous inverse, the two subordinated CPPoK with various distributional properties were studied.
Abstract: In this article, the compound Poisson processes of order $k$ (CPPoK) is introduced and its properties are discussed. Further, using mixture of tempered stable subordinator (MTSS) and its right continuous inverse, the two subordinated CPPoK with various distributional properties are studied. It is also shown that space and tempered space fractional versions of CPPoK and PPoK can be obtained, which generalize the results in the literature.

3 citations

Journal ArticleDOI
TL;DR: In this paper, the authors studied the box-counting dimension of sets related to subordinators (non-decreasing Levy processes) and proved a central limit theorem for this dimension.
Abstract: This work looks at the box-counting dimension of sets related to subordinators (non-decreasing Levy processes). It was recently shown in Savov (Electron Commun Probab 19:1–10, 2014) that almost surely $$\lim _{\delta \rightarrow 0}U(\delta )N(t,\delta ) = t$$ , where $$N(t,\delta )$$ is the minimal number of boxes of size at most $$ \delta $$ needed to cover a subordinator’s range up to time t, and $$U(\delta )$$ is the subordinator’s renewal function. Our main result is a central limit theorem (CLT) for $$N(t,\delta )$$ , complementing and refining work in Savov (2014). Box-counting dimension is defined in terms of $$N(t,\delta )$$ , but for subordinators we prove that it can also be defined using a new process obtained by shortening the original subordinator’s jumps of size greater than $$\delta $$ . This new process can be manipulated with remarkable ease in comparison with $$N(t,\delta )$$ , and allows better understanding of the box-counting dimension of a subordinator’s range in terms of its Levy measure, improving upon Savov (2014, Corollary 1). Further, we shall prove corresponding CLT and almost sure convergence results for the new process.

3 citations

Journal ArticleDOI
TL;DR: In this article, the authors compared the shape of pairwise default correlations of the Hull & White, the Gaussian copula and the Mai & Scherer model with compound Poisson process as Levy subordinator.
Abstract: In this paper, some analytical results related to the Hull & White dynamic model of credit portfolio of N obligors in the case of constant jump size are provided. For instance, this specific assumption combined with the moment generating function of the Poisson process lead to analytical calibration for the model with respect to the underlying CDSs. Further, extremely simple analytical expressions are obtained for first-to-default swaps; the more general case of quantities related to nth-to-default swaps also have a closed form and remain tractable for small n. Similarly, pairwise correlation between default indicators also proves to be simple. Although the purpose of this note is not to compare models, we compare the shape of pairwise default correlations of the Hull & White, the Gaussian copula and the Mai & Scherer model with compound Poisson process as Levy subordinator. It is shown that only the models including jumps can lead to non-vanishing default correlation for short-term maturities. Further, these models can generate higher default correlation levels compared to the Gaussian one. When calibrated on default probability of first default time, Jump-based models also lead to much higher default probability for the last obligor to default. Finally, we tackle the problem of simultaneous jumps, which prevent the above class of models to be usable when recoveries are name-specific. To that end, we propose a tractable compromise to deal with baskets being non-homogeneous recovery-wise under the Hull & White model by splitting isolated and non-isolated default events.

3 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202330
202242
202160
202056
201969
201845