Backward stochastic Volterra integral equations with jumps in a general filtration

In this paper, we study backward stochastic Volterra integral equations introduced in the papers of Lin 2002 and of Yong in 2006 and extend the existence, uniqueness or comparison results for general filtration as in Papapantoleon et al. (not only Brownian-Poisson setting). We also consider $L^p$-data and explore the time regularity of the solution, which is also new in this jump setting.

Predictable solution for reflected BSDEs when the obstacle is not right-continuous

In the present paper, we consider reflected backward stochastic differential equations when the reflecting obstacle is not necessarily right-continuous in a general filtration that supports a one-dimensional Brownian motion and an independent Poisson random measure. We prove the existence and uniqueness of a predictable solution for such equations under the stochastic Lipschitz coefficient by using the predictable Mertens decomposition.

Reflected BSDEs with general filtration and two completely separated barriers

We consider reflected backward stochastic differential equations, with two barriers, defined on probability spaces equipped with filtration satisfying only the usual assumptions of right-continuity and completeness. As for barriers, we assume that there are càdlàg processes of class D that are completely separated. We prove the existence and uniqueness of solutions for an integrable final condition and an integrable monotone generator. An application to the zero-sum Dynkin game is given.

Determination of Transmission Coefficient for the Filtration Deposit Made of Coal Grains

The study presents the method of determining constant coefficient b2, occurring in general filtration equation (1), in the second part of the denominator, that is in the expression for deposit resistance In the considerations, lack of the deposit’s compressibility was assumed, which means that the deposit porosity is constant. With such an assumption, constant coefficient b2 is equivalent with transmission coefficient, which occurs in commonly known and accepted equation – as the baseline equation – for fluid flow through a porous layer according to Darcy (Piecuch 2009, 2010). This study is another publication in the cycle of basic tests of the filtration process which constitute next publications of the authors, published in Rocznik Ochrona Środowiska [Annual Set the Environmental Protection] as well as in the magazine Gospodarka Surowcami Mineralnymi [Mineral Resources Management], to which the reader interested in these problems can refer. Another study will be the publication discussing the filtration process with the creation of sediment on the filtration deposit, hence in the general filtration equation (1) the value of sediment resistance RO will appear in the denominator. Relevant cycle of publications will study the possibilities of use of gravitational deposit filters in which the porous deposit will be the set of coal grains, while the fed mixture will also be the post-production suspension of coal grains.