Let {S t H, t ≥ 0） be a linear combination of a Brownian motion and an independent sub-fractional Brownian motion with Hurst index 0 〈 H 〈 1. Its main properties are studied. They suggest that SH lies between the ...Let {S t H, t ≥ 0） be a linear combination of a Brownian motion and an independent sub-fractional Brownian motion with Hurst index 0 〈 H 〈 1. Its main properties are studied. They suggest that SH lies between the sub-fractional Brownian motion and the mixed fractional Brownian motion. We also determine the values of H for which SH is not a semi-martingale.展开更多
We study a second-order parabolic equation with divergence form elliptic operator,having a piecewise constant diffusion coefficient with two points of discontinuity.Such partial differential equations appear in the mo...We study a second-order parabolic equation with divergence form elliptic operator,having a piecewise constant diffusion coefficient with two points of discontinuity.Such partial differential equations appear in the modelization of diffusion phenomena in medium consisting of three kinds of materials.Using probabilistic methods,we present an explicit expression of the fundamental solution under certain conditions.We also derive small-time asymptotic expansion of the PDE’s solutions in the general case.The obtained results are directly usable in applications.展开更多
文摘Let {S t H, t ≥ 0） be a linear combination of a Brownian motion and an independent sub-fractional Brownian motion with Hurst index 0 〈 H 〈 1. Its main properties are studied. They suggest that SH lies between the sub-fractional Brownian motion and the mixed fractional Brownian motion. We also determine the values of H for which SH is not a semi-martingale.
基金supported by the National Science Foundation of USA (Grant No. DMS1206276)National Natural Science Foundation of China (Grant No. 1128101)the Research Unit of Tunisia (Grant No. UR11ES53)
文摘We study a second-order parabolic equation with divergence form elliptic operator,having a piecewise constant diffusion coefficient with two points of discontinuity.Such partial differential equations appear in the modelization of diffusion phenomena in medium consisting of three kinds of materials.Using probabilistic methods,we present an explicit expression of the fundamental solution under certain conditions.We also derive small-time asymptotic expansion of the PDE’s solutions in the general case.The obtained results are directly usable in applications.
