Integration by Parts Formulae for Wiener Measures on a Path Space between two Curves

This paper is concerned with the integration by parts formulae for the pinned or the standard Wiener measures restricted on a space of paths staying between two curves. The boundary measures, concentrated on the set of paths touching one of the curves once, are specified. Our approach is based on the polygonal approximations. In particular, to establish the convergence of boundary terms, a uniform estimate is derived by means of comparison argument for a sequence of random walks conditioned to stay between two polygons. Applying the Brascamp–Lieb inequality, the stochastic integrals of Wiener type are constructed relative to the three-dimensional Bessel bridge or the Brownian meander. Supported in part by the JSPS Grant (B)(1)14340029     

The stability of stochastic partial differential equations II

We prove general results on stability (in finite time intervals) of SPDEs (stochastic partial differential equations) with unbounded coefficients, with respect to the simultaneous perturbations of the driving semimartingales, of all data, and of the underlying probability space. Hence we derive support theorems for SPDEs (with unbounded coefficients). In particular, we get theorems on supports and theorems on robustness for the nonlinear filter of diffusion processes with unbounded drift and diffusion coefficients. (The above results were proved in the case of bounded coefficients in our earlier papers [4] and [5].) Finally we treat an application in a problem of kinematic dynamo     

Backward uniqueness and the existence of the spectral limit for linear parabolic SPDEs

The aim of this article is to study the asymptotic behavior for large times of solutions of linear stochastic partial differential equations of parabolic type. In particular, we will prove the backward uniqueness result and the existence of the spectral limit for abstract SPDEs and then show how these results can be applied to linear SPDEs.     

Stochastic modeling of unresolved scales in complex systems

Model uncertainties or simulation uncertainties occur in mathematical modeling of multiscale complex systems, since some mechanisms or scales are not represented (i.e., ‘unresolved’) due to a lack in our understanding of these mechanisms or limitations in computational power. The impact of these unresolved scales on the resolved scales needs to be parameterized or taken into account. A stochastic scheme is devised to take the effects of unresolved scales into account, in the context of solving nonlinear partial differential equations. An example is presented to demonstrate this strategy. Dedicated to Professor Peter E. Kloeden on the occasion of his 60th birthday     

Higher-order stochastic partial differential equations with branching noises

In this paper, we propose a class of higher-order stochastic partial differential equations (SPDEs) with branching noises. The existence of weak (mild) solutions is established through weak convergence and tightness arguments.      

Critical review on recent developments in solventless techniques for extraction of analytes

The most recent contributions on solventless extraction techniques have been reviewed. This paper deals with those techniques that use solid phases, such as solid-phase microextraction, liquid phases, such as single-drop microextraction and hollow-fibre liquid-phase microextraction, and subcritical fluids, such as subcritical water extraction. In all cases, the most recent publications have been critically studied. Direct extraction and derivatization processes to facilitate the extraction of analytes in different areas have been included. Hyphenated approaches, if available, are also included in this review. Comparison of techniques organized by analytes and matrices also enhances this critical overview of solventless techniques.     

Vector analysis for Dirichlet forms and quasilinear PDE and SPDE on metric measure spaces

Starting with a regular symmetric Dirichlet form on a locally compact separable metric space X$X$, our paper studies elements of vector analysis, _Lp$L_p$-spaces of vector fields and related Sobolev spaces. These tools are then employed to obtain existence and uniqueness results for some quasilinear elliptic PDE and SPDE in variational form on X$X$ by standard methods. For many of our results locality is not assumed, but most interesting applications involve local regular Dirichlet forms on fractal spaces such as nested fractals and Sierpinski carpets.