Rigorous definitions of all these objects in terms of Riemann sums are given below. These definitions were motivated by [RW97], where corresponding definitions were given for usual Levy processes. There is a number of differences between the classical and the free case. First, the free increments property implies that Stπ = 0 unless π is a noncrossing partition. Second, the point of the analysi...

Molecular discreteness is apparent in small-volume chemical systems, such as biological cells, leading to stochastic kinetics. Here we present a theoretical framework to understand the effects of discreteness on the steady state of a monostable chemical reaction network. We consider independent realizations of the same chemical system in compartments of different volumes. Rate equations ignore ...

We develop the formalism for a PIM-based functional for stochastic tomography with a Kalman filter, in which the inversion problem associated with four-dimensional ionospheric stochastic tomography is regularized. For consistency, GPS data is used to select dynamically the best PIM parameters, in a 3DVAR fashion. We demonstrate the ingestion of GPS (IGS and GPS/MET) data into a parameterized io...

a rare case of non-puerperal uterine inversion caused by a large fundal leiomyoma in a 39-year nulliparous, infertile woman resulting in intractable hemorrhage was reported after a myomectomy. attempts to reduce the inversion vaginally by transecting the anterior and posterior cervix were unsuccessful and a laparotomy was performed. the inversion was not successfully corrected and hysterectomy ...

the direct way to access the petrophysical property of hydrocarbon reservoir is based on well data but due to its high cost, the seismic data has been used to obtain these parameters. for this purpose, many different methods are available and each has its own advantages and limitations. from these methods the seismic inversion is the best tool to study the reservoir characterization. the outcom...

Aalto University, P.O. Box 11000, FI-00076 Aalto www.aalto.fi Author Matti Leinonen Name of the doctoral dissertation On applying stochastic Galerkin finite element method to electrical impedance tomography Publisher School of Science Unit Department of Mathematics and Systems Analysis Series Aalto University publication series DOCTORAL DISSERTATIONS 135/2015 Field of research Mathematics Manus...

Reservoir characterization has a leading role in the reservoir geophysics and reservoir management. Since the interests of the reservoir geophysics and reservoir managements are the elastic properties and reservoir properties of the subsurface rock for their purposes, a robust method is required for converting seismic data into elastic properties. Accordingly, by employing a rock physics model ...

in this paper, a high-order and conditionally stable stochastic difference scheme is proposed for the numerical solution of $rm ithat{o}$ stochastic advection diffusion equation with one dimensional white noise process. we applied a finite difference approximation of fourth-order for discretizing space spatial derivative of this equation. the main properties of deterministic difference schemes,...