In what follows, we consider the relation between Aldous's extended convergence and weak convergence of nitrations. We prove that, for a sequence (Xn) of J_t^n)-special semimartingales, with canonical decompositio...In what follows, we consider the relation between Aldous's extended convergence and weak convergence of nitrations. We prove that, for a sequence (Xn) of J_t^n)-special semimartingales, with canonical decomposition Xn = Mn + An, if the extended convergence (Xn.Jrn)→ (X,F.) holds with a quasi-left continuous (Ft)-special semimartingale X = M + A, then, under an additional assumption of uniform integrability,we get the convergence in probability under the Skorokhod topology: Mn→M and An→A.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In what follows, we consider the relation between Aldous's extended convergence and weak convergence of nitrations. We prove that, for a sequence (Xn) of J_t^n)-special semimartingales, with canonical decomposition Xn = Mn + An, if the extended convergence (Xn.Jrn)→ (X,F.) holds with a quasi-left continuous (Ft)-special semimartingale X = M + A, then, under an additional assumption of uniform integrability,we get the convergence in probability under the Skorokhod topology: Mn→M and An→A.
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.
