Homogeneous stochastic processes

Time-homogeneous Affine State Processes for Stochastic Partial Differential Equations

The goal of this paper is to clarify for which starting points the state processes of a stochastic partial differential equation with an affine realization are time-homogeneous. We will illustrate our results by means of the HJMM equation from mathematical finance.

Generating Homogeneous Poisson Processes

We present an overview of existing methods to generate pseudorandom numbers from homogeneous Poisson processes. We provide three well-known definitions of the homogeneous Poisson process, present results that form the basis of various existing generation algorithms, and provide algorithm listings. With the intent of guiding users seeking an appropriate algorithm for a given setting, we note the...

Homogeneous fragmentation processes

The purpose of this work is to define and study homogeneous fragmentation processes in continuous time, which are meant to describe the evolution of an object that breaks down randomly into pieces as time passes. Roughly, we show that the dynamics of such a fragmentation process are determined by some exchangeable measure on the set of partitions of �, and result from the combination of two dif...

Stochastic Homogenization on Homogeneous Spaces

Motivated by inhomogeneous scaling of left invariant Riemannian metrics on a Lie group G, we consider a family of stochastic differential equations (SDEs) on G with Markov operators L = 1 ∑ k(Ak) 2 + 1 A0 + Y0, where > 0, {Ak} generates a sub Lie-algebra h of the Lie algebra g, and Y0 ∈ g. Assuming that G/H is a reductive homogeneous space, in the sense of Nomizu, we take → 0 and study the asym...

Stochastic Processes