arXiv research

The paper proves the concavity of entropy power for diffusion equations and applies it to new inequalities.

Upper bounds on constants for Brownian motion with sticky boundary.

Paper proposes Sinkformers for Transformers with doubly stochastic attention.

Proves existence of solutions for a specific nonlinear equation on Riemannian manifolds.

This paper extends ResNet theory to infinitely deep networks, linking them to diffusion processes.

This paper discusses properties of a Doubly Stochastic Poisson Process (DSPP) where the intensity process belongs to a class of affine diffusions. For any intensity process from this class we derive an analytical expression for probability distribution functions of the corresponding DSPP. A specification of our results…

We study a doubly reflected backward stochastic differential equation (BSDE) with integrable parameters and the related Dynkin game. When the lower obstacle $L$ and the upper obstacle $U$ of the equation are completely separated, we construct a unique solution of the doubly reflected BSDE by pasting local solutions and…

I$^2$SB learns nonlinear diffusion processes between images.

Doubly SGD improves convergence for intractable objective optimization.

Automated denoising score matching handles nonlinear diffusion processes.

We present new extensions to a method for constructing several families of solvable one-dimensional time-homogeneous diffusions whose transition densities are obtainable in analytically closed-form. Our approach is based on a dual application of the so-called diffusion canonical transformation method that combines smoo…

Bäcklund transformations for smooth and ``space discrete'' Hashimoto surfaces are discussed and a geometric interpretation is given. It is shown that the complex curvature of a discrete space curve evolves with the discrete nonlinear Schrödinger equation (NLSE) of Ablowitz and Ladik, when the curve evolves with the Has…

Develops a method for causal inference with noisy confounders.

Proposes a robust method for counterfactual classification.

We present a probabilistic framework for nonlinearities, based on doubly truncated Gaussian distributions. By setting the truncation points appropriately, we are able to generate various types of nonlinearities within a unified framework, including sigmoid, tanh and ReLU, the most commonly used nonlinearities in neural…

First, classes of Markov processes that scale exactly with a Hurst exponent H are derived in closed form. A special case of one class is the Tsallis density, advertised elsewhere as nonlinear diffusion or diffusion with nonlinear feedback. But the Tsallis model is only one of a very large class of linear diffusion with…

New algorithm learns nonlinear phenomena from noisy local measurements without data exchange.

SOAD model improves data assimilation for nonlinear systems.

Finslerian graph neural networks recover nonlinear diffusion geometry

FDSKL algorithm trains vertically partitioned data with kernels securely and efficiently.

The goal is to re-examine and extend the findings from the recent paper by Dumitrescu, Quenez and Sulem (2017) who studied game options within the nonlinear arbitrage-free pricing approach developed in El Karoui and Quenez (1997). We consider the setup introduced in Kim, Nie and Rutkowski (2018) where contracts of an A…

This paper proposes and analyzes a novel clustering algorithm that combines graph-based diffusion geometry with techniques based on density and mode estimation. The proposed method is suitable for data generated from mixtures of distributions with densities that are both multimodal and have nonlinear shapes. A crucial …

In this paper we introduce a simple continuous-time asset pricing framework, based on general multi-dimensional diffusion processes, that combines semi-analytic pricing with a nonlinear specification for the market price of risk. Our framework guarantees existence of weak solutions of the nonlinear SDEs under the physi…

Improved generative models for rare events using nonlinear diffusion.

Diffusion models tackle noisy inverse problems with posterior sampling.

G-FuNK learns solutions for nonlinear PDEs on multiple domains and parameters.

Global solutions found for certain reaction-diffusion equations on specific manifolds.

Develops a robust method for image reconstruction from limited data.

This work uses diffusion models for accurate signal recovery from semi-parametric models.

Proposes a neural network method to combine nonprobability and probability survey samples.

Proposes a new method for data assimilation using closed-form conditional diffusion models.

The paper tackles data-driven optimal control of unknown nonlinear systems using RKHS.

Most previous contributions to BSDEs, and the related theories of nonlinear expectation and dynamic risk measures, have been in the framework of continuous time diffusions or jump diffusions. Using solutions of BSDEs on spaces related to finite state, continuous time Markov chains, we develop a theory of nonlinear expe…

EnSF improves accuracy in tracking high-dimensional nonlinear systems.

MELD model clusters data at multiple scales, improving understanding of latent structure.

Diffusion maps are an emerging data-driven technique for non-linear dimensionality reduction, which are especially useful for the analysis of coherent structures and nonlinear embeddings of dynamical systems. However, the computational complexity of the diffusion maps algorithm scales with the number of observations. T…

StrADiff separates sources from mixtures without labels, using structured priors.

Method uses deep learning to estimate traffic intensity.

DoubleGen addresses bias in generative modeling of counterfactuals.

The paper develops a computational method for efficient online filtering of diffusion processes.

We consider a special family of occupation-time derivatives, namely proportional step options introduced by Linetsky in [Math. Finance, 9, 55--96 (1999)]. We develop new closed-form spectral expansions for pricing such options under a class of nonlinear volatility diffusion processes which includes the constant-elastic…

Study shows neural operators can efficiently solve complex reaction-diffusion systems.

Method solves Bayesian inverse problems in function space without assuming log-concavity.

Let $(M,g)$ be a complete non-compact Riemannian manifold with the $m$-dimensional Bakry-Émery Ricci curvature bounded below by a non-positive constant. In this paper, we give a localized Hamilton-type gradient estimate for the positive smooth bounded solutions to the following nonlinear diffusion equation \[ u_t=Δu-\n…

Finite-time extinction and smoothing effects in fractional fast diffusion on manifolds.

Blade uses diffusion priors to accurately and calibratedly infer complex systems.

The paper studies a 1D diffusion equation with nonlinear Robin boundary conditions and finds conditions for global and finite time blow-up or blow-down.

Novel method estimates complex nonlinear systems with stochastic differential equations.