相关论文: Holomorphic jump-diffusions

We introduce Functional Diffusion Processes (FDPs), which generalize score-based diffusion models to infinite-dimensional function spaces. FDPs require a new mathematical framework to describe the forward and backward dynamics, and several…

We show the existence of a broad class of affine Markov processes in the cone of positive self-adjoint Hilbert-Schmidt operators. Such processes are well-suited as infinite dimensional stochastic volatility models. The class of processes we…

The characteristic functions of multivariate Feller processes with generator of affine type, and with smooth symbol functions have an explicit representation in terms of power series with rational number coefficients and with monmoms…

Recent advances in infinite-dimensional diffusion models have demonstrated their effectiveness and scalability in function generation tasks where the underlying structure is inherently infinite-dimensional. To accelerate inference in such…

The diffusion model has demonstrated promising results in image generation, recently becoming mainstream and representing a notable advancement for many generative modeling tasks. Prior applications of the diffusion model for both fast…

This work focuses on a class of stochastic Hamiltonian type jump diffusion systems with state-dependent switching, in which the switching component has countably infinite many states. First,the existence and uniqueness of the underlying…

A physically more adequate definition of a quaternionic holomorphic (H-holomorphic) function of one quaternionic variable compared to known ones and a quaternionic generalization of Cauchy-Riemann's equations are presented. At that a class…

We consider nonparametric invariant density and drift estimation for a class of multidimensional degenerate resp. hypoelliptic diffusion processes, so-called stochastic damping Hamiltonian systems or kinetic diffusions, under anisotropic…

A complex potential is a holomorphic function $\Omega:\mathbb{C} \to \mathbb{C}$ whose real and imaginary parts generate a pair of orthogonal foliations, representing the equipotential lines and the streamlines of $\dot{z} =…

Probabilistic diffusion models enjoy increasing popularity in the deep learning community. They generate convincing samples from a learned distribution of input images with a wide field of practical applications. Originally, these…

Consider a one-dimensional exclusion process with finite-range translation-invariant jump rates with non-zero drift. Let the process be stationary with product Bernoulli invariant distribution at density \rho. Place a second class particle…

We consider sequences of additive functionals of difference approximations for uniformly non-degenerate multidimensional diffusions. The conditions are given, sufficient for such a sequence to converge weakly to a W-functional of the…

The density property for a Stein manifold X implies that the group of holomorphic diffeomorphisms of X is infinite-dimensional and, in a certain well-defined sense, as large as possible. We prove that if G is a complex semisimple Lie group…

In the last decades affine algebraic varieties and Stein manifolds with big (infinite-dimensional) automorphism groups have been intensively studied. Several notions expressing that the automorphisms group is big have been proposed. All of…

We establish existence of exponential moments and the validity of the affine transform formula for affine jump-diffusions with a general closed convex state space. This extends known results for affine jump-diffusions with a canonical state…

Diffusion-based image generators can now produce high-quality and diverse samples, but their success has yet to fully translate to 3D generation: existing diffusion methods can either generate low-resolution but 3D consistent outputs, or…

We describe a procedure for the generation of functional digraphs up to isomorphism; these are digraphs with uniform outdegree 1, also called mapping patterns, finite endofunctions, or finite discrete-time dynamical systems. This procedure…

Diffusion models have recently achieved remarkable success in generative modeling, yet they are commonly formulated as black-box stochastic systems with limited interpretability and few structural guarantees. In this paper, we establish a…

We provide a classification of Fueter-regular quaternionic functions $f$ in terms of the degree of complex linearity of their real differentials $df$. Quaternionic imaginary units define orthogonal almost-complex structures on the tangent…

We consider the solution of initial value problems within the context of hybrid systems and emphasise the use of high precision approximations (in software for exact real arithmetic). We propose a novel algorithm for the computation of…