Model Selection for Random Functions with Bounded Range: Applications in Science and Engineering

Field, Richard V.; Grigoriu, Mircea

doi:10.1007/978-1-4614-7385-5_15

Cited by 1 publication

(3 citation statements)

References 14 publications

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“…then y(t) = x(t) for t > T m N m = T, being y(t) and x(t) the solutions of systems of size m formulated in ( 6)- (7) with g m (t) given in (8) and (14), respectively. Notice that from the hypothesis of induction, one gets…”

Section: System With a Finite Number Of Impulses With Different Inten...mentioning

confidence: 99%

“…Theorem 1. The solution y(t) of system ( 6)- (7) where g m (t), m = 1, … , n, is defined by (8), and the solution and x(t) of system (14) with initial condition given in (15) with m = 1, … , n match for t > T n N n = T. In particular, both systems have as equilibrium point the null vector.…”

Section: System With a Finite Number Of Impulses With Different Inten...mentioning

confidence: 99%

“…To face this challenge, one relies on inverse uncertainty quantification techniques [9,12,13]. As pointed out in the literature, overall, the theory for RDEs is much less advanced than for SDEs [12, p. 258], despite the effectiveness of RDEs in modeling biological phenomena, as they are more realistic than SDEs because they allow for the use of non-Gaussian patterns and bounded stochastic processes [14,15]. It is important to underline that we shall only consider RDEs throughout this paper and they will be treated in the so-called pathwise or sample-path senses.…”

Section: Introductionmentioning

confidence: 99%

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Probabilistic analysis of a class of compartmental models formulated by random differential equations

Bevia,

Carlos Cortés,

Luisovna Pérez

et al. 2024

Math Methods in App Sciences

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This paper deals with the probabilistic analysis of a class of compartmental models formulated via a system of linear differential equations with time‐dependent non‐homogeneous terms. For the sake of generality, we assume that initial conditions and rates between compartments are random variables with arbitrary distributions while the source terms defining the flows entering the compartments are stochastic processes. We then take extensive advantage of the so‐called random variable transformation (RVT) technique to determine the first probability distribution of the solution of such a randomized model under very general hypotheses. In the simplest but relevant case of time‐independent source terms, we also obtain the probability distribution of the equilibrium, which is a random vector. Furthermore, we first particularize the aforementioned results for different types of integrable source terms that permit obtaining an explicit solution of the compartmental model: random constants, a train of Dirac delta impulses with random intensities, and a Wiener process. Secondly, we show an alternative approach based on the Liouville–Gibbs equation, which is useful when dealing with source terms that do not admit a closed‐form primitive. All the previous theoretical results are first illustrated through several numerical examples and simulations where a wide range of different probability distributions are assumed for the model parameters. The paper concludes by applying a compartmental model that describes the dynamics of oral drug administration through multiple chronologically spaced doses using synthetic data generated according to pharmacological references.

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Section: System With a Finite Number Of Impulses With Different Inten...mentioning

confidence: 99%

Section: System With a Finite Number Of Impulses With Different Inten...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Probabilistic analysis of a class of compartmental models formulated by random differential equations

Bevia,

Carlos Cortés,

Luisovna Pérez

et al. 2024

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

Model Selection for Random Functions with Bounded Range: Applications in Science and Engineering

Cited by 1 publication

References 14 publications

Probabilistic analysis of a class of compartmental models formulated by random differential equations

Probabilistic analysis of a class of compartmental models formulated by random differential equations

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