One of the most challenging aspects of the microstructural evolution in polycrystalline materials is to understand the role of topological reconfigurations during coarsening. In this paper, we study these critical events in a one-dimensional grain-boundary system and a stochastic framework for modeling texture evolution. The model is based on a master equation derived from numerically determine...

In this paper, we consider learning of spatio-temporal processes by formulating a Gaussian process model as a solution to an evolution type stochastic partial differential equation. Our approach is based on converting the stochastic infinite-dimensional differential equation into a finite dimensional linear time invariant (LTI) stochastic differential equation (SDE) by discretizing the process ...

Evolution equations of the joint response-excitation probability density function (REPDF) generalize the existing PDF evolution equations and enable us to compute the PDF of the solution of stochastic systems driven by colored random noise. This paper aims at developing an efficient numerical method for this evolution equation of REPDF by considering the response and excitation spaces separatel...

In recent years evolution of level sets of two-dimensional functions or images in time through a partial differential equation has emerged as an important tool in image processing. Curve evolutions, which may be viewed as an evolution of a single level curve, has been applied to a wide variety of problems such as smoothing of shapes, shape analysis and shape recovery. We give a stochastic inter...

As a Generalization to [37] where the dimension-free Harnack inequality was established for stochastic porous media equations, this paper presents analogous results for a large class of stochastic evolution equations with general monotone drifts. Some ergodicity, compactness and contractivity properties are established for the associated transition semigroups. Moreover, the exponential converge...

It is long known that the Fokker-Planck equation with prescribed constant coefficients of diffusion and linear friction describes the ensemble average of the stochastic evolutions in velocity space of a Brownian test particle immersed in a heat bath of fixed temperature. Apparently, it is not so well known that the same partial differential equation, but now with constant coefficients which are...

It is long known that the Fokker-Planck equation with prescribed constant coefficients of diffusion and linear friction describes the ensemble average of the stochastic evolutions in velocity space of a Brownian test particle immersed in a heat bath of fixed temperature. Apparently, it is not so well known that the same partial differential equation, but now with constant coefficients which are...

Surfaces eroded by ion sputtering are sometimes observed to develop morphologies which are either ripple (periodic) or rough (nonperiodic). We introduce a discrete stochastic model that allows us to interpret these experimental observations within a unified framework. We find that a periodic ripple morphology characterizes the initial stages of the evolution, whereas the surface displays self-a...

Inbreeding avoidance and asymmetric competition over resources have both been identified as factors favouring the evolution of sex-biased dispersal. It has also been recognized that sex-specific costs of dispersal would select for sex-biased dispersal, but there is little quantitative information on this aspect. In this paper we explore (i) the quantitative relationship between cost-asymmetry a...

For an arbitrary Hilbert space-valued Ornstein-Uhlenbeck process we construct the Ornstein-Uhlenbeck Bridge connecting a given starting point x and an endpoint y provided y belongs to a certain linear subspace of full measure. We derive also a stochastic evolution equation satisfied by the OU Bridge and study its basic properties. The OU Bridge is then used to investigate the Markov transition ...