Many situations of physical and biological interest involve diffusions on manifolds. It is usually assumed that irregularities in the geometry of these manifolds do not influence diffusions. The validity of this assumption is put to test by studying Brownian motions on nearly flat 2D surfaces. It is found by perturbative calculations that irregularities in the geometry have a cumulative and dra...

The objective of this paper is to present an algorithm, for exact simulation of a class of Ito’s diffusions. We demonstrate that when the algorithm is applicable, it is also straightforward to simulate diffusions conditioned to hit specific values at predetermined time instances. We also describe a method that exploits the properties of the algorithm to carry out inference on discretely observe...

This paper is concerned with an approachable haematopoietic stem cells model with a delay and diffusions. The stability of the equilibria are first considered by analyzing the distribution of the roots of associated characteristic equation. We then consider the impact of the diffusions on bifurcated periodic solution, and find that only small diffusions effect on the numbers of the Hopf bifurca...

Many situations of physical and biological interest involve diffusions on manifolds. It is usually assumed that irregularities in the geometry of these manifolds do not influence diffusions. The validity of this assumption is put to test by studying Brownian motions on nearly flat 2D surfaces. It is found by perturbative calculations that irregularities in the geometry have a cumulative and dra...

Abstract From the Poisson–Dirichlet diffusions to Z -measure diffusions, they all have explicit transition densities. We show that densities of can also be expressed as a mixture sequence probability measures on Thoma simplex. The coefficients are same in diffusions. This fact will uncovered by dual process method special case where established through an up–down chain Young graph.

Diffusions are useful for image processing and computer vision because they provide a convenient way of smoothing noisy data, analyzing images at multiple scales, and enhancing discontinuities. A number of diffusions of image brightness have been defined and studied so far; they may be applied to scalar and vector-valued quantities that are naturally associated with intervals of either the real...

Recently, several authors have studied maps where a function, describing the local diffusion matrix of a diffusion process with a linear drift towards an attraction point, is mapped into the average of that function with respect to the unique invariant measure of the diffusion process, as a function of the attraction point. Such mappings arise in the analysis of infinite systems of diffusions i...

We prove Cameron-Martin type quasi-invariance results for the heat kernel measure of infinite-dimensional Kolmogorov and related diffusions. first study quantitative functional inequalities appropriate finite-dimensional approximations these diffusions, we hold with dimension-independent coefficients. Applying an approach developed by Baudoin, Driver, Gordina, Melcher previously, uniform bounds...

Anisotropic diffusion is posed as a process of minimizing an energy function. Its global convergence behavior is determined by the shape of the energy surface, and its local behavior is described by an orthogonal decomposition with the decomposition coefficients being the eigenvalues of the local energy function. A sufficient condition for its convergence to a global minimum is given and is ide...