Linear and Nonlinear Ultraparabolic Equations of Kolmogorov Type Arising in Diffusion Theory and in Finance

Lanconelli, Ermanno; Pascucci, Andrea; Polidoro, Sergio

doi:10.1007/978-1-4615-0701-7_14

Cited by 66 publications

(56 citation statements)

References 26 publications

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“…Solutions of ultra-parabolic equations and the related properties have been studied in the literature (see [19] for a recent survey). Especially, it has been shown in [10] that (2.5) admits a unique fundamental solution if a satisfies the following hypotheses:…”

Section: A Propagation Of Chaos Results For Stochastic Lagrangian Modelsmentioning

confidence: 99%

Stochastic Lagrangian method for downscaling problems in computational fluid dynamics

Bernardin¹,

Bossy²,

Chauvin³

et al. 2010

ESAIM: M2AN

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Abstract. This work aims at introducing modelling, theoretical and numerical studies related to a new downscaling technique applied to computational fluid dynamics. Our method consists in building a local model, forced by large scale information computed thanks to a classical numerical weather predictor. The local model, compatible with the Navier-Stokes equations, is used for the small scale computation (downscaling) of the considered fluid. It is inspired by Pope's works on turbulence, and consists in a so-called Langevin system of stochastic differential equations. We introduce this model and exhibit its links with classical RANS models. Well-posedness, as well as mean-field interacting particle approximations and boundary condition issues are addressed. We present the numerical discretization of the stochastic downscaling method and investigate the accuracy of the proposed algorithm on simplified situations.Mathematics Subject Classification. 65C20, 65C35, 68U20, 35Q30.

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Section: A Propagation Of Chaos Results For Stochastic Lagrangian Modelsmentioning

confidence: 99%

Stochastic Lagrangian method for downscaling problems in computational fluid dynamics

Bernardin¹,

Bossy²,

Chauvin³

et al. 2010

ESAIM: M2AN

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“…Пiзнiше їх застосовували до вивчення багатьох явищ механiки, бiологiї, фiзики, економiки [2,7]. Вивченню задачi Кошi, мiшаних задач та властивостей їх розв'язкiв при-свяченi, зокрема, працi [2,8,10,11,12].…”

Section: вступunclassified

Асимптотична поведiнка розв'язку оберненої задачі для слабко нелінійного ультрапараболічного рівняння

Protsakh¹

2013

Carpathian Math. Publ.

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Розглянуто обернену задачу з iнтегральною умовою перевизначення для слабко нелiнiйно-го ультрапараболiчного рiвняння з невiдомим, залежним вiд часу, множником правої частини цього рiвняння. Знайдено умови, за яких узагальнений розв'язок задачi прямує до нуля при зростаннi часової змiнної.Ключовi слова i фрази: обернена задача, ультрапараболiчне рiвняння, узагальнений розв'я-зок.

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“…This kind of operator has been extensively studied (see [11] and [12] for a comprehensive bibliography …”

Section: Example 14 (Kolmogorov-type Operators) Assumementioning

confidence: 99%

Harnack Inequalities and Gaussian Estimates for a Class of Hypoelliptic Operators

Polidoro

2005

Progress in Nonlinear Differential Equations and Their Applications

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Linear and Nonlinear Ultraparabolic Equations of Kolmogorov Type Arising in Diffusion Theory and in Finance

Cited by 66 publications

References 26 publications

Stochastic Lagrangian method for downscaling problems in computational fluid dynamics

Stochastic Lagrangian method for downscaling problems in computational fluid dynamics

Асимптотична поведiнка розв'язку оберненої задачі для слабко нелінійного ультрапараболічного рівняння

Harnack Inequalities and Gaussian Estimates for a Class of Hypoelliptic Operators

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