相关论文: Representation Theorems for Quadratic ${\cal F}$-C…
Dependently typed proof assistant rely crucially on definitional equality, which relates types and terms that are automatically identified in the underlying type theory. This paper extends type theory with definitional functor laws,…
Complementing the analysis in [41], we investigate the well-posedness of SPDEs problems of doubly nonlinear type. These arise ubiquitously in the modelization of dissipative media and correspond to generalized balance laws between…
We establish a martingale-type characterisations for the continuum Gaussian free field (GFF) and for fractional Gaussian free fields (FGFs), using their connection to the stochastic heat equation and to fractional stochastic heat equations.…
Given a category C of a combinatorial nature, we study the following fundamental question: how does the combinatorial behavior of C affect the algebraic behavior of representations of C? We prove two general results. The first gives a…
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…
We introduce a notion of nonlinear expectation --G--expectation-- generated by a nonlinear heat equation with infinitesimal generator G. We first discuss the notion of G-standard normal distribution. With this nonlinear distribution we can…
Let $F$ be a $p$-adic field. Let $\mathcal{R}$ be the Grothendieck ring of complex smooth finite-length representations of the groups $\{GL_n(F)\}_{n=0}^\infty$ taken together, with multiplication defined in the sense of parabolic…
In this paper, we assume that the filtration $\bb F$ is generated by a $d$-dimensional Brownian motion $W=(W_1,\cdots,W_d)'$ as well as an integer-valued random measure $\mu(du,dy)$. The random variable $\ttau$ is the default time and $L$…
This article introduces a novel nonparametric methodology for Generalized Linear Models which combines the strengths of the binary regression and latent variable formulations for categorical data, while overcoming their disadvantages.…
When the \textit{martingale representation property} holds, we call any local martingale which realizes the representation a \textit{representation process}. There are two properties of the \textit{representation process} which can greatly…
A predictive distribution over a sequence of $N+1$ events is said to be "frequency mimicking" whenever the probability for the final event conditioned on the outcome of the first $N$ events equals the relative frequency of successes among…
Based on a recent development in the area of error control coding, we introduce the notion of convolutional factor graphs (CFGs) as a new class of probabilistic graphical models. In this context, the conventional factor graphs are referred…
The hyperfinite $G$-expectation is a nonstandard discrete analogue of $G$-expectation (in the sense of Robinsonian nonstandard analysis). A lifting of a continuous-time $G$-expectation operator is defined as a hyperfinite $G$-expectation…
We establish necessary and sufficient conditions for the N-representability of the universal one-electron reduced density matrix functional. Functionals satisfying these conditions are guaranteed to yield variational upper bounds on the…
Consider additive functionals of a Markov chain $W_k$, with stationary (marginal) distribution and transition function denoted by $\pi$ and $Q$, say $S_n=g(W_1)+...+g(W_n)$, where $g$ is square integrable and has mean 0 with respect to…
In material science, models are derived to predict emergent material properties (e.g. elasticity, strength, conductivity) and their relations to processing conditions. A major drawback is the calibration of model parameters that depend on…
A variational principle for Lagrangian densities containing derivatives of real order is formulated and the invariance of this principle is studied in two characteristic cases. Necessary and sufficient conditions for an infinitesimal…
While Conformal Prediction (CP) has proven to be a powerful framework for uncertainty quantification, guaranteeing conditional coverage remains a central challenge. Although finite-sample, distribution-free conditional validity is known to…
A new derivative, called deformable derivative, is introduced here which is equivalent to ordinary derivative in the sense that one implies other. The deformable derivative is defined using limit approach like that of ordinary one but with…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…