Related papers: A Mean-Reverting SDE on Correlation matrices
We introduce a novel notion of divergence between continuous martingales; the reciprocal specific relative entropy. First, we motivate this definition from multiple perspectives. Thereafter, we solve the reciprocal specific relative entropy…
In [1], we introduced a new, matrix algebraic, performance analysis framework for wireless systems with fading channels based on the matrix exponential distribution. The main idea was to use the compact, powerful, and easy-to-use, matrix…
The renormalization group transformation for extreme value statistics of independent, identically distributed variables, recently introduced to describe finite size effects, is presented here in terms of a partial differential equation…
In this paper, we study an optimal mean-variance investment-reinsurance problem for an insurer (she) under a Cram\'er-Lundberg model with random coefficients. At any time, the insurer can purchase reinsurance or acquire new business and…
Diffusion models, typically formulated as discretizations of stochastic differential equations (SDEs), have achieved state-of-the-art performance in generative tasks. However, their theoretical analysis often involves complex proofs. In…
Mathematical mean-field approaches have been used in many fields, not only in Physics and Chemistry, but also recently in Finance, Economics, and Game Theory. In this paper we will study a new special mean-field problem in a purely…
The usefulness of recursive equations to compute scattering matrix elements for arbitrary processes is discussed. Explicit results at tree and one-loop order, obtained by the HELAC/PHEGAS package that is based on the Dyson-Schwinger…
We present a method for approximating solutions of Stochastic Differential Equations (SDEs) with arbitrary rates. This approximation is derived for bounded and measurable test functions. Specifically, we demonstrate that, leveraging the…
Weak convergence of maxima of dependent sequences of identically distributed continuous random variables is studied under normalizing sequences arising as subsequences of the normalizing sequences from an associated iid sequence. This…
Diffusion processes are a class of stochastic differential equations (SDEs) providing a rich family of expressive models that arise naturally in dynamic modelling tasks. Probabilistic inference and learning under generative models with…
We consider a fully discrete and explicit scheme for the mean curvature flow of boundaries, based on an elementary diffusion step and a precise redistancing operation. We give an elementary convergence proof for the scheme under the…
A new class of explicit Euler schemes, which approximate stochastic differential equations (SDEs) with superlinearly growing drift and diffusion coefficients, is proposed in this article. It is shown, under very mild conditions, that these…
Let $X$ be a regular one-dimensional transient diffusion and $L^y$ be its local time at $y$. The stochastic differential equation (SDE) whose solution corresponds to the process $X$ conditioned on $[L^y_{\infty}=a]$ for a given $a\geq 0$ is…
We establish a process level large deviation principle for systems of interacting Bessel-like diffusion processes. By establishing weak uniqueness for the limiting non-local SDE of McKean-Vlasov type, we conclude that the latter describes…
A Wishart kernel density estimator (KDE) is introduced for density estimation in the cone of positive definite matrices. The estimator is boundary-aware and mitigates the boundary bias suffered by conventional KDEs, while remaining simple…
We show that for general-type self-adjoint and skew-self-adjoint Dirac systems on the semi-axis Weyl functions are unique analytic extensions of the reflection coefficients. New results on the extension of the Weyl functions to the real…
The optimization of the latents and parameters of diffusion models with respect to some differentiable metric defined on the output of the model is a challenging and complex problem. The sampling for diffusion models is done by solving…
We develop a class of non-Gaussian translation processes that extend classical stochastic differential equations (SDEs) by prescribing arbitrary absolutely continuous marginal distributions. Our approach uses a copula-based transformation…
Score-based diffusion models have emerged as one of the most promising frameworks for deep generative modelling, due to their state-of-the art performance in many generation tasks while relying on mathematical foundations such as stochastic…
We derive dispersion estimates for solutions of a one-dimensional discrete Dirac equations with a potential. In particular, we improve our previous result, weakening the conditions on the potential. To this end we also provide new results…