In this paper, we first study a purely discontinuous Girsanov transform which is more general than that studied in Chen and Song [(2003), J. Funct. Anal. 201, 262–281]. Then we show that the transition density of any purely discontinuous Girsanov transform of a symmetric stable process is comparable to the transition density of the symmetric stable process. The same is true for the Girsanov tra...

Abstract Nine characteristics of discontinuous agreement are shown to flow from a syntax that deals in whole phi structures and linearisation algorithm renders these when conditions converge. This approach is demonstrably superior reliance solely on syntax, morphology, or the lexicon, outperforming across range morphological syntactic data Afroasiatic languages those Australia Papua New Guinea.

Empirical investigations ([1], [2]) showed that purely discontinuous Lévy processes allow more realistic modeling of financial time series. We present a new class of bond price models that can be driven by a wide range of Lévy processes (Lt). We do not just replace Brownian motion (Bt) in the standard diffusion model for the price of a zero coupon bond with maturity T dP (t, T ) = P (t, T )(r(t...

We show that the increments of generalized Wiener process, useful to describe nonGaussian white noise sources, have the properties of infinitely divisible random processes. Using functional approach and the new correlation formula for non-Gaussian white noise we derive directly from Langevin equation, with such a random source, the Kolmogorov’s equation for Markovian non-Gaussian process. From ...

We review the Dudley integral for Belyaev dichotomy applied to Gaussian processes on spheres, and discuss approximate (or restricted) continuity of paths in discontinuous case. also spatio-temporal case, sphere cross line. In continuous we investigate link between smoothness decay rate angular power spectrum, following Tauberian work first author, Malyarenko, Lang Schwab.

Through an idealized model of a partial differential equation with discontinuous “on-off” switches in the forcing term, we investigate the effect of the model error generated by the traditional discretization of discontinuous physical “on-off” processes on the variational data assimilation (VDA) in detail. Meanwhile, the validity of the adjoint approach in the VDA with “on-off” switches is also...

The aim of this paper is to provide a unified treatment of the existence of solution of both upper and lower semicontinuous quantum stochastic differential inclusions. The quantum stochastic differential inclusion is driven by operatorvalued stochastic processes lying in certain metrizable locally convex space. The unification of solution sets to these two discontinuous non-commutative stochast...

In this paper we study the Martin boundary of open sets with respect to a large class of purely discontinuous symmetric Lévy processes in R. We show that, if D ⊂ R is an open set which is κ-fat at a boundary point Q ∈ ∂D, then there is exactly one Martin boundary point associated with Q and this Martin boundary point is minimal. AMS 2010 Mathematics Subject Classification: Primary 60J50, 31C40;...

We discuss the problem of trapping and mobilization of nonwetting fluids during immiscible two-phase displacement processes in porous media. Capillary desaturation curves give residual saturations as a function of capillary number. Interpreting capillary numbers as the ratio of viscous to capillary forces the breakpoint in experimental curves contradicts the theoretically predicted force balanc...