Stochastic Modeling of Indoor Air Temperature

Janczura, Joanna; Maciejewska, Monika; Szczurek, Andrzej; Wyłomańska, Agnieszka

doi:10.1007/s10955-013-0794-9

Cited by 11 publications

(10 citation statements)

References 32 publications

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“…Tempered stable distributions are particularly important in applications due to the fact that they can be in the same time close to α-stable distributions and posses finite moments of all orders. From the above Laplace transform one can infer relation between probability density functions (PDFs) of pure α-stable (g T S ) and tempered stable (g T T ) distributions, namely [17] g T T (x) = e −λx+λ α g T S (x).…”

Section: Modelmentioning

confidence: 99%

“…They were used in variety of physical systems, including charge carrier transport in amorphous semiconductors [8,9,10], transport in micelles [11], intracellular transport [12] or motion of mRNA molecules inside E. coli cells [13]. The behaviour corresponding to continuous time random walk scenario can be also observed in stock prices or interest rates data [14,15] as well as in the time series related to indoor air quality parameters [16,17,18].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Modified cumulative distribution function in application to waiting time analysis in the continuous time random walk scenario

Połoczański

Wyłomańska

Maciejewska

et al. 2016

J. Phys. A: Math. Theor.

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The continuous time random walk model plays an important role in modeling of so called anomalous diffusion behaviour. One of the specific property of such model are constant time periods visible in trajectory. In the continuous time random walk approach they are realizations of the sequence called waiting times. The main attention of the paper is paid on the analysis of waiting times distribution. We introduce here novel methods of estimation and statistical investigation of such distribution. The methods are based on the modified cumulative distribution function. In this paper we consider three special cases of waiting time distributions, namely α-stable, tempered stable and gamma. However the proposed methodology can be applied to broad set of distributions -in general it may serve as a method of fitting any distribution function if the observations are rounded. The new statistical techniques we apply to the simulated data as well as to the real data describing CO 2 concentration in indoor air.

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Section: Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Modified cumulative distribution function in application to waiting time analysis in the continuous time random walk scenario

Połoczański

Wyłomańska

Maciejewska

et al. 2016

J. Phys. A: Math. Theor.

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“…where β > 0, 0 < γ < 1. The tempered stable subordinator has been considered in many applications like finance [38] and indoor air quality [22]. For the tempered stable subordinator the memory kernel takes the following form [39]:…”

Section: Tempered Stable Subordinatormentioning

confidence: 99%

“…On the other hand, the tempered stable process is an extension of the Brownian motion but is non-Gaussian; therefore, it can be used for many real applications, especially with behavior typical for the intermediate case between Gaussian and stable. The tempered stable process has found many practical applications, for instance in physics [16,17], biology [18], finance [20,21] and indoor air quality problems [22].…”

Section: Introductionmentioning

confidence: 99%

The tempered stable process with infinitely divisible inverse subordinators

Wyłomańska¹

2013

J. Stat. Mech.

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In the last decade processes driven by inverse subordinators have become extremely popular. They have been used in many different applications, especially for data with observable constant time periods. However, the classical model, i.e. the subordinated Brownian motion, can be inappropriate for the description of observed phenomena that exhibit behavior not adequate for Gaussian systems. Therefore, in this paper we extend the classical approach and replace the Brownian motion by the tempered stable process. Moreover, on the other hand, as an extension of the classical model, we analyze the general class of inverse subordinators. We examine the main properties of the tempered stable process driven by inverse subordinators from the infinitely divisible class of distributions. We show the fractional Fokker-Planck equation of the examined process and the asymptotic behavior of the mean square displacement for two cases of subordinators. Additionally, we examine how an external force can influence the examined characteristics.

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“…For some data in real life, such as biology [3], financial time series [4], ecology [5], and physics [6], the time-changed stochastic process is needed, where the deterministic time variable is replaced by a positive non-decreasing random process and thus a combination of two independent random processes is produced. One of the processes is called external process (or the original process), and another one is called internal process (or a subordinator).…”

Section: Introductionmentioning

confidence: 99%

Tempered fractional Langevin–Brownian motion with inverseβ-stable subordinator

Chen¹,

Wang²,

Deng³

2018

J. Phys. A: Math. Theor.

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Time-changed stochastic processes have attracted great attention and wide interests due to their extensive applications, especially in financial time series, biology and physics. This paper pays attention to a special stochastic process, tempered fractional Langevin motion, which is non-Markovian and undergoes ballistic diffusion for long times. The corresponding time-changed Langevin system with inverse β-stable subordinator is discussed in detail, including its diffusion type, moments, Klein-Kramers equation, and the correlation structure. Interestingly, this subordination could result in both subdiffusion and superdiffusion, depending on the value of β. The difference between the subordinated tempered fractional Langevin equation and the subordinated Langevin equation with external biasing force is studied for a deeper understanding of subordinator. The time-changed tempered fractional Brownian motion by inverse β-stable subordinator is also considered, as well as the correlation structure of its increments. Some properties of the statistical quantities of the time-changed process are discussed, displaying striking differences compared with the original process.

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Stochastic Modeling of Indoor Air Temperature

Cited by 11 publications

References 32 publications

Modified cumulative distribution function in application to waiting time analysis in the continuous time random walk scenario

Modified cumulative distribution function in application to waiting time analysis in the continuous time random walk scenario

The tempered stable process with infinitely divisible inverse subordinators

Tempered fractional Langevin–Brownian motion with inverseβ-stable subordinator

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