Related papers: Optional Decomposition for continuous semimartinga…
This paper deals with asset price bubbles modeled by strict local martingales. With any strict local martingale, one can associate a new measure, which is studied in detail in the first part of the paper. In the second part, we determine…
Assume that we are given a filtration $(\mathscr F_n)$ on a probability space $(\Omega,\mathscr F,\mathbb P)$ of the form that each $\mathscr F_n$ is generated by the partition of one atom of $\mathscr F_{n-1}$ into two atoms of $\mathscr…
A maxitive measure is the analogue of a finitely additive measure or charge, in which the usual addition is replaced by the supremum operation. Contrarily to charges, maxitive measures often have a density. We show that maxitive measures…
In this note we generate two local median oscillation decompositions of an arbitrary measurable function and discuss some applications to Calder\'{o}n-Zygmund singular integral operators $T$. These applications rely on the inequality…
We present a generalisation of the theory of iterated function systems and associated fractals to the setting of noncommutative geometry. Along the way, we discuss some ideas surrounding locally compact noncommutative metric spaces.
We prove almost global existence for semilinear wave equations outside of nontrapping obstacles. We use the vector field method, but only use the generators of translations and Euclidean rotations. Our method exploits 1/r decay of wave…
In this paper we establish a complete representation theorem for $G$-martingales. Unlike the existing results in the literature, we provide the existence and uniqueness of the second order term, which corresponds to the second order…
We discuss the theoretical framework required for the computation of radiative corrections to semileptonic decay rates in lattice simulations, and in particular to those for $K_{\ell3}$ decays. This is an extension of the framework we have…
The paper establishes an analog Whittaker-Shannon-Kotelnikov sampling theorem with fast decreasing coefficient, as well as a new modification of the corresponding interpolation formula applicable for general type non-vanishing bounded…
Az\'{e}ma associated with an honest time L the supermartingale $Z_{t}^{L}=\mathbb{P}[L>t|\mathcal{F}_{t}]$ and established some of its important properties. This supermartingale plays a central role in the general theory of stochastic…
Stricker's theorem states that a Gaussian process is a semimartingale in its natural filtration if and only if it is the sum of an independent increment Gaussian process and a Gaussian process of finite variation, see [1983, Z. Wahrsch.…
We study the behaviour of infinitesimal deformation functors of local group actions with regard to passing to subgroups and quotient groups. Inspired by the cohomological information, we conjecture the existence of a decomposition of a…
Martingale representation theorem for set-valued martingales was proposed by M. Kisielewicz [J. Math. Anal. Appl. 2014]. We shall prove that the result holds only for very special case: the set-valued martingale degenerates to the…
We provide martingale analogs of weakly cancelling differential operators and prove a Sobolev-type embedding theorem for these operators in the martingale setting.
In this paper we explain that the natural filtration of a continuous Hunt process is continuous, and show that martingales over such a filtration are continuous. We further establish a martingale representation theorem for a class of…
We provide a general Doob-Meyer decomposition for $g$-supermartingale systems, which does not require any right-continuity on the system. In particular, it generalizes the Doob-Meyer decomposition of Mertens (1972) for classical…
This paper studies an equity market of stochastic dimension, where the number of assets fluctuates over time. In such a market, we develop the fundamental theorem of asset pricing, which provides the equivalence of the following statements:…
We exhibit conditions under which the flow of marginal distributions of a discontinuous semimartingale $\xi$ can be matched by a Markov process, whose infinitesimal generator is expressed in terms of the local characteristics of $\xi$. Our…
We derive equivalent conditions for the (local) absolute continuity of two laws of semimartingales on random sets. Our result generalizes previous results for classical semimartingales by replacing a strong uniqueness assumption by a weaker…
The applications of the partial fraction decomposition in control and systems engineering are several. In this letter, we propose a new interpretation of residues in the partial fraction decomposition, which is employed for the following…