Related papers: Variance-Gamma (VG) model: Fractional Fourier Tran…
This paper develops a European option pricing formula for fractional market models. Although there exist option pricing results for a fractional Black-Scholes model, they are established without accounting for stochastic volatility. In this…
The one-point probability distribution function (pdf) of the large-scale density field is an important tool to follow the evolution of cosmological structures. In this paper we present a new model for this pdf for all regimes and all…
Support Vector Machines (SVMs) are an important tool for performing classification on scattered data, where one usually has to deal with many data points in high-dimensional spaces. We propose solving SVMs in primal form using feature maps…
The calculation of the band-gap by density-functional theory (DFT) methods is examined by considering the behavior of the energy as a function of number of electrons. It is found that the incorrect band-gap prediction with most approximate…
Time Series Foundation Models (TSFMs) have emerged as a promising approach for zero-shot financial forecasting, demonstrating strong transferability and data efficiency gains. However, their adoption in financial applications is hindered by…
Computing partition function is the most important statistical inference task arising in applications of Graphical Models (GM). Since it is computationally intractable, approximate methods have been used to resolve the issue in practice,…
Fr\'echet mean and variance provide a way of obtaining mean and variance for general metric space valued random variables and can be used for statistical analysis of data objects that lie in abstract spaces devoid of algebraic structure and…
In many applications, we collect independent samples from interconnected populations. These population distributions share some latent structure, so it is advantageous to jointly analyze the samples. One effective way to connect the…
Given the importance of continuous-time stochastic volatility models to describe the dynamics of interest rates, we propose a goodness-of-fit test for the parametric form of the drift and diffusion functions, based on a marked empirical…
Reward factorization personalizes large language models (LLMs) by decomposing rewards into shared basis functions and user-specific weights. Yet, existing methods estimate user weights from scarce data in isolation and as deterministic…
The Gaussian Graphical Model (GGM) is a popular tool for incorporating sparsity into joint multivariate distributions. The G-Wishart distribution, a conjugate prior for precision matrices satisfying general GGM constraints, has now been in…
We present a discrete time stochastic volatility model in which the conditional distribution of the logreturns is a Variance-Gamma, that is a normal variance-mean mixture with Gamma mixing density. We assume that the Gamma mixing density is…
Reliable and interpretable traffic crash modeling is essential for understanding causality and improving road safety. This study introduces a novel approach to predicting collision types by utilizing a comprehensive dataset fused from…
The fractional Fourier transform (FrFT), a fundamental operation in physics that corresponds to a rotation of phase space by any angle, is also an indispensable tool employed in digital signal processing for noise reduction. Processing of…
We propose a simpler derivation of the probability density function of Feller Diffusion using the Fourier Transform and solving the resulting equation via the Method of Characteristics. We also discuss simulation algorithms and confirm key…
This paper proposes a multivariable extremum seeking scheme using Fast Fourier Transform (FFT) for a network of subsystems working towards optimizing the sum of their local objectives, where the overall objective is the only available…
Fractal structure of a system suggests the optimal way in which parts arranged or put together to form a whole. The ideas from fractals have a potential application to the researches on urban sustainable development. To characterize fractal…
Full tensor gravity (FTG) devices provide up to five independent components of the gravity gradient tensor. However, we do not yet have a quantitative understanding of which tensor components or combinations of components are more important…
In this paper, we propose a novel approach for generating music based on an artificial intelligence (AI) system. We analyze the features of music and use them to fit and predict the music. The fractional Fourier transform (FrFT) and the…
We propose Functional Flow Matching (FFM), a function-space generative model that generalizes the recently-introduced Flow Matching model to operate in infinite-dimensional spaces. Our approach works by first defining a path of probability…