Stochastics and Stochastics Reports 

About: Stochastics and Stochastics Reports is an academic journal. The journal publishes majorly in the area(s): Stochastic differential equation & Differential equation. It has an ISSN identifier of 1026-7794. Over the lifetime, 630 publications have been published receiving 16445 citations.

Backward stochastic differential equations and integral-partial differential equations

Abstract: We consider a backward stochastic differential equation, whose data (the final condition and the coefficient) are given functions of a jump-diffusion process. We prove that under mild conditions the solution of the BSDE provides a viscosity solution of a system of parabolic integral-partial differential equations. Under an additional assumption, that system of equations is proved to have a unique solution, in a given class of continuous functions

Equivalent martingale measures and no-arbitrage in stochastic securities market models

Abstract: We characterize those vector-valued stochastic processes (with a finite index set and defined on an arbitrarystochasic base) which can become a martingale under an equivalent change of measure.This question is important in a widely studied problem which arises in the theory of finite period securities markets with one riskless bond and a finite number of risky stocks. In this setting, our characterization gives a criterion for recognizing when a securities market model allows for no arbitrage opportunities (free lunches). Intuitively, this can be interpreted as saying if one cannot win betting on a process, then it must be a martingale under an equivalent measure, and provides a converse to the classical notion that one cannot win betting on a martingale.

Random attractors for the 3D stochastic Navier-Stokes equation with multiplicative white noise

Abstract: The random attractor to the stochastic 3D Navier-Stokes equation will be studied. In the first part we formulate an existence theorem for attractors of non-autonomous dynamical systems on a bundle of metric spaces. Using this theorem we can prove the existence of an attractor for the 3D Navier-Stokes equation with multiplicative white noise. In addition we prove that this attractor is a random multi-function

Brownian Models of Open Queueing Networks with Homogeneous Customer Populations

Abstract: We consider a family of multidimensional diffusion processes that arise as heavy traffic approximations for open queueing networks. More precisely, the diffusion processes considered here arise as approximate models of open queueing networks with homogeneous customer populations, which means that customers occupying any given node or station of the network are essentially indistinguishable from one another. The classical queueing network model of J. R. Jackson fits this description, as do other more general types of systems, but multiclass network models do not.The objectives of this paper are (a) to explain in concrete terms how one approximates a conventional queueing model or a real physical system by a corresponding Brownian model, and (b) to state and prove some new results regarding stationary distributions of such Brownian models. The part of the paper aimed at objective (a) is largely a recapitulation of previous work on weak convegence theorems, with the emphasis placed on modeling intuition. Wit...