Pairs of complementary transmission conditions for Brownian motion
نویسندگان
چکیده
Abstract Following our previous work on complementary boundary conditions, we write Cartesian product of two copies a space continuous functions the real line as direct sum subspaces that are invariant under cosine family operators underlying Brownian motion. Both these formed by pairs extensions functions: in first subspace form is shaped unequivocally transmission conditions describing snapping out motion, second, it skew motion with certain degree stickiness. In this sense, above to each other.
منابع مشابه
A probabilistic interpretation of the transmission conditions using the Skew Brownian motion
In order to solve with a Monte Carlo method a parabolic (or elliptic) PDE with a transmission condition, we need to understand the behavior of the stochastic process when it reaches a point where this tranmission condition holds. In this article, we show that a process called the Skew Brownian motion can be helpful to understand how to deal with this kind of problem in a one-dimensional media. ...
متن کاملDiffusion Equation and Complementary Schrodinger’s Equation from Brownian Motion
Diffusion Equation and classical Schrödinger Equation have been derived from Brownian motion and the quantum limits have been derived, which transform the classical Schrödinger equation in to usual quantum equation without any formal analytic continuation and waveparticle duality. These quantum limits have been shown to lead to Heisenberg uncertainty relation between position and momentum of th...
متن کاملExact solutions for Fokker-Plank equation of geometric Brownian motion with Lie point symmetries
In this paper Lie symmetry analysis is applied to find new solution for Fokker Plank equation of geometric Brownian motion. This analysis classifies the solution format of the Fokker Plank equation.
متن کاملLimiting Behaviors for Brownian Motion Reflected on Brownian Motion
Suppose that g(t) and Wt are independent Brownian motions starting from g(0) = W0 = 0. Consider the Brownian motion Yt reflected on g(t), obtained from Wt by the means of the Skorohod lemma. The upper and lower limiting behaviors of Yt are presented. The upper tail estimate on exit time is computed via principal eigenvalue.
متن کاملBrownian Brownian Motion – I
A classical model of Brownian motion consists of a heavy molecule submerged into a gas of light atoms in a closed container. In this work we study a 2D version of this model, where the molecule is a heavy disk of mass M ≫ 1 and the gas is represented by just one point particle of mass m = 1, which interacts with the disk and the walls of the container via elastic collisions. Chaotic behavior of...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematische Annalen
سال: 2023
ISSN: ['1432-1807', '0025-5831']
DOI: https://doi.org/10.1007/s00208-023-02613-x