کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
7377087 | 1480112 | 2016 | 10 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Kinetic and mean field description of Gibrat's law
ترجمه فارسی عنوان
توضیحات جنبشی و متوسط به قانون جبرات
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کلمات کلیدی
مدلهای جنبشی، قانون جبرات، معادلات دیفرانسیل خطی، رفتار طولانی مدت،
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
فیزیک ریاضی
چکیده انگلیسی
I introduce and analyze a linear kinetic model that describes the evolution of the probability density of the number of firms in a society, in which the microscopic rate of change obeys to the so-called law of proportional effect proposed by Gibrat (1930, 1931). Despite its apparent simplicity, the possible mean field limits of the kinetic model are varied. In some cases, the asymptotic limit can be described by a first-order partial differential equation. In other cases, the mean field equation is a linear diffusion with a non constant diffusion coefficient that can be studied analytically, by virtue of a transformation of variables recently utilized in Iagar and Sánchez (2013) to study the heat equation in a nonhomogeneous medium with critical density. In this case, it is shown that the large-time behavior of the solution is represented, for a large class of initial data, by a lognormal distribution with constant mean value and variance increasing exponentially in time at a precise rate.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Physica A: Statistical Mechanics and its Applications - Volume 461, 1 November 2016, Pages 802-811
Journal: Physica A: Statistical Mechanics and its Applications - Volume 461, 1 November 2016, Pages 802-811
نویسندگان
Giuseppe Toscani,