A Dirichlet Process Characterization of a Class of Reflected Diffusions
نویسندگان
چکیده
For a general class of stochastic differential equations with reflection that admit a Markov weak solution and satisfy a certain L continuity condition, p > 1, it is shown that the associated reflected diffusion can be decomposed as the sum of a local martingale and a continuous, adapted process of zero p-variation. In particular, when p = 2, this implies that the associated reflected diffusion is a Dirichlet processes in the sense of Föllmer. As motivation for such a characterization, it is also shown that reflected diffusions belonging to a specific family within this class are not semimartingales, but are Dirichlet processes. This family of diffusions arise naturally as approximations of certain stochastic networks that use the so-called generalized processor sharing scheduling policy.
منابع مشابه
Countable Representation for Infinite Dimensional Diffusions Derived from the Two-parameter Poisson-dirichlet Process
This paper provides a countable representation for a class of infinite-dimensional diffusions which extends the infinitely-many-neutral-alleles model and is related to the two-parameter PoissonDirichlet process. By means of Gibbs sampling procedures, we define a reversible Moran-type population process. The associated process of ranked relative frequencies of types is shown to converge in distr...
متن کاملIntroducing of Dirichlet process prior in the Nonparametric Bayesian models frame work
Statistical models are utilized to learn about the mechanism that the data are generating from it. Often it is assumed that the random variables y_i,i=1,…,n ,are samples from the probability distribution F which is belong to a parametric distributions class. However, in practice, a parametric model may be inappropriate to describe the data. In this settings, the parametric assumption could be r...
متن کاملOn Product-form Stationary Distributions for Reflected Diffusions with Jumps in the Positive Orthant
In this paper we study the stationary distributions for reflected diffusions with jumps in the positive orthant. Under the assumption that the stationary distribution possesses a density in R+ that satisfies certain finiteness conditions, we characterize the Fokker-Planck equation. We then provide necessary and sufficient conditions for the existence of a product-form distribution for diffusion...
متن کاملOptimal Reflection of Diffusions and Barrier Options Pricing under Constraints
We introduce a new class of control problems in which the gain depends on the solution of a stochastic differential equation reflected at the boundary of a bounded domain, along directions which are controlled by a bounded variation process. We provide a PDE characterization of the associated value function. This study is motivated by applications in mathematical finance where such equations ar...
متن کاملExistence Results for a Dirichlet Quasilinear Elliptic Problem
In this paper, existence results of positive classical solutions for a class of second-order differential equations with the nonlinearity dependent on the derivative are established. The approach is based on variational methods.
متن کامل