arXiv research

Study on determinants of unitary Brownian motion and their asymptotic laws.

Geodesic walks converge to Brownian motion on Finsler manifolds.

Quaternionic Brownian motion on flag manifold linked to sphere diffusion.

FDBM models use fractional Brownian motion to model complex stochastic processes.

Estimates spectral gap for Brownian motion on sticky-reflecting domains.

Upper bounds on constants for Brownian motion with sticky boundary.

Study bounds for Brownian motion on manifolds with sticky boundary conditions.

Optimizes dividend policies in a Brownian model with controlled rates.

Analyzed a generalized voter model with power-law herding intensity, revealing anomalous diffusion and long-range memory.

We consider a one-parameter family of Grushin-type singularities on surfaces, and discuss the possible diffusions that extend Brownian motion to the singularity. This gives a quick proof and clear intuition for the fact that heat can only cross the singularity for an intermediate range of the parameter. When crossing i…

The Epps effect helps distinguish between continuous and discrete financial tick data.

This paper constructs Brownian motion on complex flag manifolds and finds joint distribution of stochastic areas.

Study parameter sensitivities in bond pricing models with jumps.

Study of most probable paths for anisotropic Brownian motions on manifolds.

A standard Variational Autoencoder, with a Euclidean latent space, is structurally incapable of capturing topological properties of certain datasets. To remove topological obstructions, we introduce Diffusion Variational Autoencoders with arbitrary manifolds as a latent space. A Diffusion Variational Autoencoder uses t…

We provide a complete characterization of the class of one-dimensional time-homogeneous diffusions consistent with a given law at an exponentially distributed time using classical results in diffusion theory. To illustrate we characterize the class of diffusions with the same distribution as Brownian motion at an expon…

We derive the joint density of a Skew Brownian motion, its last visit to the origin, local and occupation times. The result is applied to option pricing in a two valued local volatility model and in a displaced diffusion model with constrained volatility.

This work extends Tweedie's formulae to non-Gaussian processes for better diffusion model generation.

New model learns graph spectra accurately, outperforming existing methods.

Efficient diffusion model for symmetric manifolds reduces training and computation costs.

New method identifies drift and diffusivity from SDE marginals.

This paper explains how predictable order flow can lead to Brownian motion in financial prices.

Two insurance companies collaborate to maximize the probability of none going bankrupt.

Constructs stochastic processes on sub-Riemannian manifolds using Cartan connections.

We study markets with no riskless (safe) asset. We derive the corresponding Black-Scholes-Merton option pricing equations for markets where there are only risky assets which have the following price dynamics: (i) continuous diffusions; (ii) jump-diffusions; (iii) diffusions with stochastic volatilities, and; (iv) geome…

We use tools from $n$-dimensional Brownian motion in conjunction with the Feynman-Kac formulation of heat diffusion to study nodal geometry on a compact Riemannian manifold $M$. On one hand we extend a theorem of Lieb and prove that any nodal domain $Ω_λ$ almost fully contains a ball of radius $\sim \frac{1}{\sqrtλ}$. …

By further developing the generalized $Γ$-calculus for hypoelliptic operators, we prove hypocoercive estimates for a large class of Kolmogorov type operators which are defined on non necessarily totally geodesic Riemannian foliations. We study then in detail the example of the velocity spherical Brownian motion, whose …

New diffusion models handle constrained domains, improving generative tasks.

Sig-DEG speeds up diffusion models by distilling them into faster approximations.

Modeling high-frequency speculative markets as auction search processes.

Study Brownian motion on Grassmann manifold using matrix stochastic calculus.

Extends diffusion-based Schrödinger bridge models to handle time-dependent potentials.

The paper connects Riemannian Gaussian distributions to random matrix theory and diffusion kernels.

The goal of this investigation was to overcome limitations of a persistency analysis, introduced by Benoit Mandelbrot for fractal Brownian processes: nondifferentiability, Brownian nature of process and a linear memory measure. We have extended a sense of a Hurst factor by consideration of a phase diffusion power law. …

Generative Fractional Diffusion Models improve image diversity and quality.

Adaptive importance sampling techniques are widely known for the Gaussian setting of Brownian driven diffusions. In this work, we want to extend them to jump processes. Our approach relies on a change of the jump intensity combined with the standard exponential tilting for the Brownian motion. The free parameters of ou…

This paper proposes and analyses a new multilevel Monte Carlo method for the estimation of mean exit times for multi-dimensional Brownian diffusions, and associated functionals which correspond to solutions to high-dimensional parabolic PDEs through the Feynman-Kac formula. In particular, it is proved that the complexi…

We solve a version of the optimal trade execution problem when the mid asset price follows a displaced diffusion. Optimal strategies in the adapted class under various risk criteria, namely value-at-risk, expected shortfall and a new criterion called "squared asset expectation" (SAE), related to a version of the cost v…

This paper proposes to model asset price dynamics with a mixture of diffusion processes where the instantaneous volatility of the underlying diffusion process contains a random vector. The marginal probability distributions of the proposed process can match exactly the risk-neutral distributions implied by both spot va…

We show by explicit closed form calculations that a Hurst exponent H that is not 1/2 does not necessarily imply long time correlations like those found in fractional Brownian motion. We construct a large set of scaling solutions of Fokker-Planck partial differential equations where H is not 1/2. Thus Markov processes, …

This paper provides guarantees for DFM models using KL divergence.

Unified geometric framework for Brownian motion on various manifolds.

The study examines a financial model with sticky prices and finds no arbitrage when interest rate is zero.

We study the radial part of sub-Riemannian Brownian motion in the context of totally geodesic foliations. Itô's formula is proved for the radial processes associated to Riemannian distances approximating the Riemannian one. We deduce very general stochastic completeness criteria for the sub-Riemannian Brownian motion. …

The mixed-fractional CEV model improves CDS pricing by accounting for default risk.

Lyons and Sullivan have shown how to discretize harmonic functions on a Riemannian manifold $M$ whose Brownian motion satisfies a certain recurrence property called $\ast$-recurrence. We study analogues of this discretization for tensor fields which are harmonic in the sense of the covariant Laplacian. We show that, un…

Innovative extensions to option pricing models using asymmetric Brownian motion and random walk approaches.

We study systems of Brownian particles on the real line, which interact by splitting the local times of collisions among themselves in an asymmetric manner. We prove the strong existence and uniqueness of such processes and identify them with the collections of ordered processes in a Brownian particle system, in which …