The space-fractional Poisson process

Orsingher, Enzo; Polito, Federico

doi:10.1016/j.spl.2011.12.018

Cited by 95 publications

(144 citation statements)

References 10 publications

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“…we can write, sinceqo(t) = 0, for t > 0, we obtain the space-fractional Poisson process N" (t), t > 0, studied in Orsingher and Polito (2012b). The distributions of jumps (1.1) and (1.2) specialize to and we note that the probabilities (4.1) can be obtained directly from (4.2).…”

Section: General Resultsmentioning

confidence: 99%

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Counting processes with Bernštein intertimes and random jumps

Orsingher¹,

Toaldo

2015

J. Appl. Probab.

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In this paper we consider point processes N f (r), t > 0, with independent increments and integer-valued jumps whose distribution is expressed in terms of Bernstein functions f with Levy measure v. We obtain the general expression of the probability generating functions Gf of N f , the equations governing the state probabilities p{ of N f , and their corresponding explicit forms. We also give the distribution of the first-passage times T! of N f , and the related governing equation. We study in detail the cases of the fractional Poisson process, the relativistic Poisson process, and the gamma-Poisson process whose state probabilities have the form of a negative binomial. The distribution of the times T? of jumps with height 1j (LJ=1 1j = k) under the condition N (t) = k for all these special processes is investigated in detail.

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Section: General Resultsmentioning

confidence: 99%

“…we obtain the space-fractional Poisson process studied in Orsingher and Polito (2012b), where f(JL) = JL a , a E (0, 1). In this case, the subordinator corresponding to the space-fractional Poisson is a positively skewed stable process of order Ct.…”

Section: Introductionmentioning

confidence: 99%

Counting processes with Bernštein intertimes and random jumps

Orsingher¹,

Toaldo

2015

J. Appl. Probab.

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“…[21] for the case ν ∈ (0, 1) and [25] for the case ν ∈ (1, ∞)). [21] for the case ν ∈ (0, 1) and [25] for the case ν ∈ (1, ∞)).…”

Section: Definitionmentioning

confidence: 99%

Fractional Discrete Processes: Compound and Mixed Poisson Representations

Beghin¹,

Macci

2014

J. Appl. Probab.

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We consider two fractional versions of a family of nonnegative integer-valued processes. We prove that their probability mass functions solve fractional Kolmogorov forward equations, and we show the overdispersion of these processes. As particular examples in this family, we can define fractional versions of some processes in the literature as the Pólya-Aeppli process, the Poisson inverse Gaussian process, and the negative binomial process. We also define and study some more general fractional versions with two fractional parameters.

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“…, 2008). Alternatively, according to DAMÉ et al (2010), is to use a data series of maximum daily rain per year from where the hydrological study will be conducted, and from this, a disaggregation model (Jennings et al, 2010;HANAISH et al, 2011;ENGIDA & ESTEVES, 2011;SAFEEQ & FARES, 2011;ORSINGHER & POLITO, 2012) to obtain rain ranges at sub-daily time intervals.…”

Section: Introductionmentioning

confidence: 99%

Analysis of the relationship intensity, duration, frequency of disaggregated daily rainfall in southern Rio Grande do Sul, Brazil

Damé¹,

Teixeira-Gandra²,

Villela³

et al. 2014

Eng. Agríc.

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ABSTRACT:The intensity, duration, and frequency relationship (IDF) of rainfall occurrence may be done through continuous records of pluviographs or daily pluviometer values . The objective of this study was to estimate the intensity-duration-frequency relationships of precipitation, using the method of daily rainfall disaggregation, at weather stations located to the southern half of the state of Rio Grande do Sul; comparing them with those obtained by rain gauge records, in places considered homogeneous from the meteorological point of view. The IDF equation parameters were estimated from daily rainfall disaggregation data, using the method of nonlinear optimization. To validate the equations confidence indices and efficiency and the "t" Student test, among maximum intensity values obtained from the disaggregated daily rainfall durations of 10; 30; 60 min and 6; 12 and 24 h and those extracted from existing IDF equations. For all studied stations and return periods, the trust index values were regarded as "optimal", i.e., greater than 0.85. The maximal intensity of rainfall obtained by daily rainfall disaggregation have similarity with those obtained by relations IDF standards. Thus, the method constitutes a feasible alternative in obtaining the IDF relationships.KEYWORDS: hydrology, daily rainfall disaggregation, heavy rain. RELAÇÃO INTENSIDADE-DURAÇÃO-FREQUÊNCIA DA PRECIPITAÇÃO PLUVIALDIÁRIA DESAGREGADA NO SUL DO RIO GRANDE DO SUL RESUMO: A obtenção da relação intensidade-duração-frequência (IDF) de ocorrência de chuvas pode ser feita mediante registros contínuos de pluviógrafos ou de valores diários de pluviômetros. O objetivo do presente trabalho foi estimar as relações intensidade-duração-frequência de chuva, utilizando a metodologia da desagregação da chuva diária, para estações localizadas na metade sul do Estado do Rio Grande do Sul, comparando-as com as obtidas mediante registros pluviográficos, em locais considerados homogêneos do ponto de vista meteorológico. Os parâmetros da equação IDF foram estimados a partir dos dados de desagregação de chuva diária, utilizando o método de otimização não linear. Para validar as equações, foram utilizados índices de confiança e de eficiência, e o teste "t" de Student, entre os valores de intensidades máximas obtidos a partir da chuva diária desagregada, nas durações de 10; 30; 60 min e 6; 12 e 24 h e aqueles extraídos de equações IDF já existentes. Para todas as estações estudadas e períodos de retorno, os valores do índice de confiança foram considerados "ótimos", ou seja, maiores do que 0,85. Os valores de intensidade máxima de precipitação pluvial obtidos por desagregação da chuva diária apresentam similaridade com os obtidos por relações IDF padrões. A metodologia de desagregação de chuva diária constitui-se em alternativa viável na obtenção das relações IDF. PALAVRAS-CHAVE:hidrologia, desagregação da chuva diária, chuva intensa.

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The space-fractional Poisson process

Cited by 95 publications

References 10 publications

Counting processes with Bernštein intertimes and random jumps

Counting processes with Bernštein intertimes and random jumps

Fractional Discrete Processes: Compound and Mixed Poisson Representations

Analysis of the relationship intensity, duration, frequency of disaggregated daily rainfall in southern Rio Grande do Sul, Brazil

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