Blending Brownian motion and heat equation

Heat Equation and Reflected Brownian Motion in Time Dependent Domains

Diffusion 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...

Exact 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.

The Heat Equation and Reflected Brownian Motion in Time-dependent Domains

The paper is concerned with reflecting Brownian motion (RBM) in domains with deterministic moving boundaries, also known as “non-cylindrical domains,” and its connections with partial differential equations. Construction is given for reflecting Brownian motion in C-smooth time-dependent domains in the n-dimensional Euclidean space R. Various sample path properties of RBM, its two-sided transiti...

The Heat Equation and Reflected Brownian Motion in Time-dependent Domains by Krzysztof Burdzy,1

The paper is concerned with reflecting Brownian motion (RBM) in domains with deterministic moving boundaries, also known as “noncylindrical domains,” and its connections with partial differential equations. Construction is given for RBM in C3-smooth time-dependent domains in the n-dimensional Euclidean space Rn. We present various sample path properties of the process, two-sided estimates for i...