Variational principles and Lagrangian functions for stochastic processes and their dissipative statistical descriptions

Giona, Massimiliano

doi:10.1016/j.physa.2017.01.024

Cited by 15 publications

(21 citation statements)

References 32 publications

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“…As a consequence of this property, the corresponding evolution operators, parametrized with respect to time t, form a group of transformations defined also for t < 0. There are several thermodynamic implications of this result, and some of them are addressed in [46].…”

Section: Physical Regularity Propertiesmentioning

confidence: 99%

“…The occurrence of a finite propagation velocity characterizing GPK processes and the associated transport models has several physical implications as regards the regularity of physical observables. Two simple paradigmatic examples are reviewed below taken from [46,47], considering for simplicity one-dimensional spatial models.…”

Section: Physical Regularity Propertiesmentioning

confidence: 99%

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Generalized Poisson--Kac Processes and the Regularity of Laws of Nature

Giona¹

2018

Acta Phys. Pol. B

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The meaning and the features of Generalized Poisson-Kac processes are analyzed in the light of their regularity properties in order to show how the finite propagation velocity, characterizing these models, permits to eliminate the occurrence of singularities in transport models. Apart from a brief overview on their spectral properties, on the regularization of boundary-value problems, and on their origin from simple Lattice Random Walk models, the article focuses on their application in the study of stochastic partial differential equations, and how their use permits to eliminate the divergence of low-order moments that characterizes the corresponding field equations in the presence of spatially δ-correlated stochastic perturbations, and to ensure positivity whenever needed. A simple reaction-diffusion system subjected to a stochastically intermitted flux and the Edwards-Wilkinson model are used to show these properties.

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Section: Physical Regularity Propertiesmentioning

confidence: 99%

Section: Physical Regularity Propertiesmentioning

confidence: 99%

Generalized Poisson--Kac Processes and the Regularity of Laws of Nature

Giona¹

2018

Acta Phys. Pol. B

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“…, 2 k min , it is possible to estimate the stationary transversal distribution of the transit point averaged over ∼10 7 -10 8 realization still using a relatively small ensemble of particles. From Equation (19), or equivalently Equation (20), the stationary transversal transit distribution p * (y) is given by…”

Section: Proofmentioning

confidence: 99%

“…The proof follows from Equations (32)- (33), by considering N(y) = √ 2 K 0 a(y), D(y) = v(y) and λ = 1/2, µ = 0. Specifically, the term involving the second-order derivative in Equation 33coincides with that Equation (20). As regards the convective contribution,…”

Section: Mixed-order Stochastic Integralsmentioning

confidence: 99%

“…Closely related to the experimental analysis, the research on stochastic methods in physics is experiencing a renewed flourishing in a variety of different directions: from the understanding of the emergent anomalous features in a variety of physical systems showing both subdiffusive and superdiffusive scalings [8,9], to the understanding of weak ergodicity breaking [10,11], to the characterization of stochastic processes possessing finite propagation velocity [12][13][14][15] and the understanding of the thermodynamic implications of this property [16][17][18][19][20]. Stochastic processes possessing bounded propagation velocity intrinsically arise in relativistic theories [21][22][23][24] and in applications involving both high-energy physics and astrophysical models [25].…”

Section: Introductionmentioning

confidence: 99%

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Space-Time Inversion of Stochastic Dynamics

2020

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This article introduces the concept of space-time inversion of stochastic Langevin equations as a way of transforming the parametrization of the dynamics from time to a monotonically varying spatial coordinate. A typical physical problem in which this approach can be fruitfully used is the analysis of solute dispersion in long straight tubes (Taylor-Aris dispersion), where the time-parametrization of the dynamics is recast in that of the axial coordinate. This allows the connection between the analysis of the forward (in time) evolution of the process and that of its exit-time statistics. The derivation of the Fokker-Planck equation for the inverted dynamics requires attention: it can be deduced using a mollified approach of the Wiener perturbations “a-la Wong-Zakai” by considering a sequence of almost everywhere smooth stochastic processes (in the present case, Poisson-Kac processes), converging to the Wiener processes in some limit (the Kac limit). The mathematical interpretation of the resulting Fokker-Planck equation can be obtained by introducing a new way of considering the stochastic integrals over the increments of a Wiener process, referred to as stochastic Stjelties integrals of mixed order. Several examples ranging from stochastic thermodynamics and fractal-time models are also analyzed.

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