Löwner evolution driven by a stochastic boundary point

Ivanov, Georgy; Vasil'ev, Alexander

doi:10.1007/s13324-011-0019-9

Cited by 9 publications

(9 citation statements)

References 25 publications

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“…The results of this part were obtained by G. Ivanov and A. Vasil'ev [286]. We considered a setup [286] in which the sample paths are represented by the trajectories of a point (e.g., the origin) in the unit disk D evolving randomly under the generalized Löwner equation.…”

Section: Generalized Löwner-kufarev Stochastic Evolutionmentioning

confidence: 99%

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Classical and Stochastic Laplacian Growth

Gustafsson

Teodorescu

Васильев

2014

Advances in Mathematical Fluid Mechanics

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More information about this series at http://www.springer.com/series/5032 Advances in Mathematical Fluid Mechanics is a forum for the publication of high quality monographs, or collections of works, on the mathematical theory of fluid mechanics, with special regards to the Navier-Stokes equations. Its mathematical aims and scope are similar to those of the Journal of Mathematical Fluid Mechanics. In particular, mathematical aspects of computational methods and of applications to science and engineering are welcome as an important part of the theory. So also are works in related areas of mathematics that have a direct bearing on fluid mechanics.The monographs and collections of works published here may be written in a more expository style than is usual for research journals, with the intention of reaching a wide audience. Collections of review articles will also be sought from time to time.

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Section: Generalized Löwner-kufarev Stochastic Evolutionmentioning

confidence: 99%

“…In [286] the authors proved the existence of a unique stationary point of Ψ t in terms of the stochastic vector field In [286] the authors proved the existence of a unique stationary point of Ψ t in terms of the stochastic vector field…”

Section: Chaptermentioning

confidence: 99%

Classical and Stochastic Laplacian Growth

Gustafsson

Teodorescu

Васильев

2014

Advances in Mathematical Fluid Mechanics

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“…We considered a setup [127] in which the sample paths are represented by the trajectories of a point (e.g., the origin) in the unit disk D evolving randomly under the generalized Löwner equation. The driving mechanism differs from SLE.…”

Section: Generalized Löwner-kufarev Stochastic Evolutionmentioning

confidence: 99%

Classical and Stochastic Löwner–Kufarev Equations

Bracci

Contreras

Díaz-Madrigal

et al. 2013

Harmonic and Complex Analysis and Its Applications

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In this paper we present a historical and scientific account of the development of the theory of the Löwner-Kufarev classical and stochastic equations spanning the 90-year period from the seminal paper by K. Löwner in 1923 to recent generalizations and stochastic versions and their relations to conformal field theory. Löwner and Kufarev and Pommerenke and Schramm and Evolution family and Subordination chain and Conformal mapping and Integrable system and Brownian motion[2010]Primary: 01A70, 30C35; Secondary: 17B68, 70H06, 81R10

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“…In recent papers Alexander Vasil'ev developed stochastic topics in complex analysis, see, e.g., [4][5][6]. In early 2014 Vasil'ev proposed the problem of studying a limit process f n → f as n → ∞ when every starlike function f n is given by (1) with |a k | ≥ 1, k = 1, .…”

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confidence: 99%

Extension of Starlike Functions to a Finitely Punctured Plane

Prokhorov¹

2017

Issues of Analysis

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Abstract. We consider a sequence of functions which are starlike in the unit disk and their logarithmic derivatives are meromorphic with a finite number of simple poles in any boundary domain. These poles are either boundary deterministic or random with given characteristics. The aim of the article is the limit process and properties of the limit functions. We distinguish conditions for residues and distribution of poles. Under certain conditions, the sequence converges to the identity function. Another conditions allow us to obtain estimates for the limit function and its logarithmic derivative.

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Löwner evolution driven by a stochastic boundary point

Cited by 9 publications

References 25 publications

Classical and Stochastic Laplacian Growth

Classical and Stochastic Laplacian Growth

Classical and Stochastic Löwner–Kufarev Equations

Extension of Starlike Functions to a Finitely Punctured Plane

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