Related papers: Affine processes are regular
Semilinear stochastic partial differential equations on bounded domains $\mathscr{D}$ are considered. The semilinear term may have arbitrary polynomial growth as long as it is continuous and monotone except perhaps near the origin. Typical…
We prove existence and uniqueness of solutions to a class of stochastic semilinear evolution equations with a monotone nonlinear drift term and multiplicative noise, considerably extending corresponding results obtained in previous work of…
In this paper, we consider a class of slow-fast systems of stochastic partial differential equations where the nonlinearity in the slow equation is not continuous and unbounded. We first provide conditions that ensure the existence of a…
Let $G$ be a subgroup of $\mathrm{SL}(\mathbb{R}^{d+1})\ltimes\mathbb{R}^{d+1}$ obtained by adding a translation part to a torsion-free discrete subgroup of $\mathrm{SL}(\mathbb{R}^{d+1})$ dividing a convex cone in the sense of Benoist. We…
As an application of Brouwer's fixed-point theorem we prove that a continuously differentiable convex function with gradient of constant norm is an affine mapping. It is a first-order characterization of affine mappings among continuously…
We establish strong well-posedness for a class of degenerate SDEs of kinetic type with autonomous diffusion driven by a symmetric $\alpha$-stable process under H\"older regularity conditions for the drift term. We partially recover the…
In this paper, we study a second order variational problem for locally convex hypersurfaces, which is the affine invariant analogue of the classical Plateau problem for minimal surfaces. We prove existence, regularity and uniqueness results…
Affine coherent states are generated by affine kinematical variables much like canonical coherent states are generated by canonical kinematical variables. Although all classical and quantum formalisms normally entail canonical variables, it…
In this paper we consider the growth, large fluctuations and memory properties of an affine stochastic functional differential equation with an average functional where the contributions of the average and instantaneous terms are…
We show that the Eisenbud-Goto conjecture holds for (homogeneous) seminormal simplicial affine semigroup rings. Moreover, we prove an upper bound for the Castelnuovo-Mumford regularity in terms of the dimension, which is similar as in the…
We generalize to the super context, the known fact that if an affine algebraic group $G$ over a commutative ring $k$ acts freely (in an appropriate sense) on an affine scheme $X$ over $k$, then the dur sheaf $X\tilde{\tilde{/}}G$ of…
We show that any semi-algebraic sweeping process admits piecewise absolutely continuous solutions, and any such bounded trajectory must have finite length. Analogous results hold more generally for sweeping processes definable in o-minimal…
The formalism recently introduced in arXiv:1610.08468 allows one to assign a regularity structure, as well as a corresponding "renormalisation group", to any subcritical system of semilinear stochastic PDEs. Under very mild additional…
For $M$ being a closed manifold or the Euclidean space we present a detailed proof of regularity properties of the composition of $H^s$-regular diffeomorphisms of $M$ for $s > 1/2\dim M + 1$.
This paper deals with the realisation of affine constraints on nonreversible stochastic differential equations (SDE) by strong confining forces. We prove that the confined dynamics converges pathwise and on bounded time intervals to the…
Point processes are stochastic models generating interacting points or events in time, space, etc. Among characteristics of these models, first-order intensity and conditional intensity functions are often considered. We focus on…
Given a morphism from an affine semigroup Q to an arbitrary commutative monoid, it is shown that every fiber possesses an affine stratification: a partition into a finite disjoint union of translates of normal affine semigroups. The proof…
Affine jump-diffusions constitute a large class of continuous-time stochastic models that are particularly popular in finance and economics due to their analytical tractability. Methods for parameter estimation for such processes require…
The affine synthesis operator is shown to map the mixed-norm sequence space $\ell^1(\ell^p)$ surjectively onto $L^p(\Rd), 1 \leq p < \infty$, assuming the Fourier transform of the synthesizer does not vanish at the origin and the…
It was recently proved that any strictly stationary stochastic process can be viewed as an autoregressive process of order one with coloured noise. Furthermore, it was proved that, using this characterisation, one can define closed form…