Pairs of complementary transmission conditions for Brownian motion
Open Access
- 7 May 2023
- journal article
- research article
- Published by Springer Nature in Mathematische Annalen
- Vol. 388 (4) , 4317-4342
Abstract
Following our previous work on complementary boundary conditions, we write Cartesian product of two copies of a space of continuous functions on the real line as the direct sum of two subspaces that are invariant under a cosine family of operators underlying Brownian motion. Both these subspaces are formed by pairs of extensions of continuous functions: in the first subspace the form of these extensions is shaped unequivocally by the transmission conditions describing snapping out Brownian motion, in the second, it is shaped by the transmission conditions of skew Brownian motion with certain degree of stickiness. In this sense, the above transmission conditions are complementary to each other.Keywords
This publication has 37 references indexed in Scilit:
- A general theorem on generation of moments-preserving cosine families by Laplace operators in C[0,1]Semigroup Forum, 2014
- On moments-preserving cosine families and semigroups in C[0, 1]Journal of Evolution Equations, 2013
- Brownian motions on metric graphsJournal of Mathematical Physics, 2012
- From a PDE model to an ODE model of dynamics of synaptic depressionDiscrete and Continuous Dynamical Systems-Series B, 2012
- Monte Carlo study of a two‐compartment exchange model of diffusionNMR in Biomedicine, 2010
- Lord Kelvin’s method of images in semigroup theorySemigroup Forum, 2010
- Generation of cosine families via Lord Kelvin’s method of imagesJournal of Evolution Equations, 2010
- Accurate particle-based simulation of adsorption, desorption and partial transmissionPhysical Biology, 2009
- On the constructions of the skew Brownian motionProbability Surveys, 2006
- Exact analytic solutions for diffusion impeded by an infinite array of partially permeable barriersProceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 1992