UTokyo Repository カテゴリ: Graduate School of Mathematical SciencesGraduate School of Mathematical Scienceshttp://hdl.handle.net/2261/1532017-06-28T03:42:51Z2017-06-28T03:42:51ZA Representation Theorem on a Filtering Model with First-Passage-Type Stopping TimeNakashima, Takenobuhttp://hdl.handle.net/2261/721782017-04-13T15:16:57Z2016-02-25T00:00:00Zタイトル: A Representation Theorem on a Filtering Model with First-Passage-Type Stopping Time
著者: Nakashima, Takenobu
抄録: We present a representation theorem for a filtering model with first-passage-type stopping time. The model is constructed from two unobservable processes and one observable process that is under the influence of two unobservable processes. A filter is constructed using Brownian motion in the observable process and a first-passage-type stopping time in an unobservable process. Though our theorems are similar to those of Nakagawa[5], we do not use pinned Brownian motion measure, which is difficult to deal with. In addition, we describe a representation theorem for another filtration that was not discussed by Nakagawa[5].2016-02-25T00:00:00ZOn the Initial Value Problem for the Navier-Stokes Equations with the Initial Datum in Critical Sobolev and Besov SpacesKhai, D. Q.Tri, N. M.http://hdl.handle.net/2261/721772017-04-13T15:13:08Z2016-02-25T00:00:00Zタイトル: On the Initial Value Problem for the Navier-Stokes Equations with the Initial Datum in Critical Sobolev and Besov Spaces
著者: Khai, D. Q.; Tri, N. M.
抄録: The existence of local unique mild solutions to the Navier-Stokes equations in the whole space with an initial tempered distribution datum in critical homogeneous or inhomogeneous Sobolev spaces is shown. Especially, the case when the integral-exponent is less than 2 is investigated. The global existence is also obtained for the initial datum in critical homogeneous Sobolev spaces with a norm small enough in suitable critical Besov spaces. The key lemma is to establish the bilinear estimates in these spaces, due to the point-wise decay of the kernel of the heat semigroup.2016-02-25T00:00:00ZA Uniform Boundedness Result for Solutions to the Liouville Type Equation with Boundary SingularityBahoura, Samy Skanderhttp://hdl.handle.net/2261/721762017-04-13T15:13:04Z2016-02-25T00:00:00Zタイトル: A Uniform Boundedness Result for Solutions to the Liouville Type Equation with Boundary Singularity
著者: Bahoura, Samy Skander
抄録: We give blow-up behavior of a sequence of solutions of a Liouville-type problem with a singular weight and Dirichlet boundary conditions. As an application we derive a compactness criterion in the same spirit of the well known Brezis-Merle’s result.2016-02-25T00:00:00ZToric Resolution of Singularities in a Certain Class of C∞ Functions and Asymptotic Analysis of Oscillatory IntegralsKamimoto, JoeNose, Toshihirohttp://hdl.handle.net/2261/721752017-04-13T15:13:02Z2016-02-25T00:00:00Zタイトル: Toric Resolution of Singularities in a Certain Class of C∞ Functions and Asymptotic Analysis of Oscillatory Integrals
著者: Kamimoto, Joe; Nose, Toshihiro
抄録: In a seminal work of A. N. Varchenko, the behavior at infinity of oscillatory integrals with real analytic phase is precisely investigated by using the theory of toric varieties based on the geometry of the Newton polyhedron of the phase. The purpose of this paper is to generalize his results to the case that the phase is contained in a certain class of C∞ functions. The key in our analysis is a toric resolution of singularities in the above class of C∞ functions. The properties of poles of local zeta functions, which are closely related to the behavior of oscillatory integrals, are also studied under the associated situation.2016-02-25T00:00:00Z