arXiv subjects

Carlos Escudero

Publications and source records attributed to Carlos Escudero.

At least 19 recordsLinked to original sources

arXiv2026

Itô versus Hänggi-Klimontovich

Interpreting the noise in a stochastic differential equation, in particular the Itô versus Stratonovich dilemma, is a problem that has generated a lot of debate in the physical literature. In the last decades, a third interpretation of noise, given by the so-called Hänggi-Klimontovich integral, has been proposed as better adapted to describe certain physical systems, particularly in statistical mechanics. Herein, we introduce this integral in a precise mathematical manner and analyze its properties, signaling those that have made it appealing within the realm of physics. Subsequently, we employ this integral to model some statistical mechanical systems, such as the random dispersal of Langevin particles and the relativistic Brownian motion. We show that, for these classical examples, the Hänggi-Klimontovich integral is worse adapted than the Itô integral and even the Stratonovich one.

math-ph↗

arXiv2026

Optimal Routing across Constant Function Market Makers with Gas Fees

We study the optimal routing problem in decentralized exchanges built on Constant Function Market Makers when trades can be split across multiple heterogeneous pools and execution incurs fixed on-chain costs (gas fees). While prior routing formulations typically abstract from fixed activation costs, real on-chain execution presents non-negligible gas fees. They also become convex under concavity/convexity assumptions on the invariant functions. We propose a general optimization framework that allows differentiable invariant functions beyond global convexity and incorporates fixed gas fees through a mixed-integer model that induces activation thresholds. Subsequently, we introduce a relaxed formulation of this model, whereby we deduce necessary optimality conditions, obtaining an explicit Karush-Kuhn-Tucker system that links prices, fees, and activation. We further establish sufficient optimality conditions using tools from generalized convexity (pseudoconcavity/pseudoconvexity and quasilinearity), yielding a verifiable optimality characterization without requiring convex trade functions. Finally, we relate the relaxed solution to the original mixed-integer model by providing explicit approximation bounds that quantify the utility gap induced by relaxation. Our results extend the mathematical theory for routing by offering no-trade conditions in fragmented on-chain markets in the presence of gas fees.

math.OC↗

arXiv2025

Beneath the kinetic interpretation of noise

Diffusion theory establishes a fundamental connection between stochastic differential equations and partial differential equations. The solution of a partial differential equation known as the Fokker-Planck equation describes the probability density of the stochastic process that solves a corresponding stochastic differential equation. The kinetic interpretation of noise refers to a prospective notion of stochastic integration that would connect a stochastic differential equation with a Fokker-Planck equation consistent with the Fick law of diffusion, without introducing correction terms in the drift. This work is devoted to identifying the precise conditions under which such a correspondence can occur. One of these conditions is a structural constraint on the diffusion tensor, which severely restricts its possible form and thereby renders the kinetic interpretation of noise a non-generic situation. This point is illustrated through a series of examples. Furthermore, the analysis raises additional questions, including the possibility of defining a stochastic integral inspired by numerical algorithms, the behavior of stochastic transport equations in heterogeneous media, and the development of alternative models for anomalous diffusion. All these topics are addressed using stochastic analytical tools similar to those employed to study the main problem: the existence of the kinetic interpretation of noise.

math.PR↗

arXiv2025

Optimal investment with insider information using Skorokhod & Russo-Vallois integration

We study the maximization of the logarithmic utility for an insider with different anticipating techniques. Our aim is to compare the utilization of Russo-Vallois forward and Skorokhod integrals in this context. Theoretical analysis and illustrative numerical examples showcase that the Skorokhod insider outperforms the forward insider. This remarkable observation stands in contrast to the scenario involving risk-neutral traders. Furthermore, an ordinary trader could surpass both insiders if a significant negative fluctuation in the driving stochastic process leads to a sufficiently negative final value. These findings underline the intricate interplay between anticipating stochastic calculus and nonlinear utilities, which may yield non-intuitive results from the financial viewpoint.

math.OC↗

arXiv2025

Stochastic cloaking: concealing a region from diffusive particles

We introduce "stochastic cloaking," where a region of space is concealed from an ensemble of diffusing particles whose individual trajectories are governed by a stochastic (Langevin) equation. Our simulations reveal how different interpretations of the Langevin equation affect the cloaking performance of an annular single-layer invisibility cloak of smoothly varying diffusivity in two dimensions. Near-perfect cloaking is achieved under the Ito convention, indicated by the cloak preventing particles from accessing an inner core without disturbing the particle density outside the cloak. The cloak's performance can be further improved by regularising its singular behaviour. We believe our demonstration of stochastic cloaking is a significant milestone, comparable to earlier developments that extended cloaking from optics and acoustics to thermodynamics.

cond-mat.mtrl-sci↗

arXiv2025

Three-level qualitative classification of financial risks under varying conditions through first passage times

This work focuses on financial risks from a probabilistic point of view. The value of a firm is described as a geometric Brownian motion and default emerges as a first passage time event. On the technical side, the critical threshold that the value process has to cross to trigger the default is assumed to be an arbitrary continuous function, what constitutes a generalization of the classical Black-Cox model. Such a generality favors modeling a wide range of risk scenarios, including those characterized by strongly time-varying conditions; but at the same time limits the possibility of obtaining closed-form formulae. To avoid this limitation, we implement a qualitative classification of risk into three categories: high, medium, and low. They correspond, respectively, to a finite mean first passage time, to an almost surely finite first passage time with infinite mean, and to a positive probability of survival for all times. This allows for an extensive classification of risk based only on the asymptotic behavior of the default function, which generalizes previously known results that assumed this function to be an exponential. However, even within these mathematical conditions, such a classification is not exhaustive, as a consequence of the behavioral freedom that continuous functions enjoy. Overall, our results contribute to the design of credit risk classifications from analytical principles and, at the same time, constitute a call of attention on potential models of risk assessment in situations largely affected by time evolution.

q-fin.MF↗

arXiv2025

Direct observation of phase change accommodating hydrogen uptake in bimetallic nanoparticles

Hydrogen holds great promise as a cleaner alternative to fossil fuels, but its efficient and affordable storage remains a significant challenge. Bimetallic systems, such as Pd-Ni, present a promising option for storing hydrogen. In this study, using the combination of different cuttingedge X-ray and electron techniques, we observed the transformations of Pd-Ni nanoparticles, which initially consist of a NiO-rich shell surrounding a Pd-rich core but undergo a major transformation when interacting with hydrogen. During the hydrogen exposure, the Pd core breaks into smaller pockets, dramatically increasing its surface area and enhancing the hydrogen storage capacity, especially in nanoparticles with lower Pd content. The findings provide deep understanding of the morphological changes at the atomic level during hydrogen storage and contribute for designing cost-effective hydrogen storage using multi-metallic systems.

cond-mat.mtrl-sci↗

arXiv2024

Time evaluation of portfolio for asymmetrically informed traders

We study the anticipating version of the classical portfolio optimization problem in a financial market with the presence of a trader who possesses privileged information about the future (insider information), but who is also subjected to a delay in the information flow about the market conditions; hence this trader possesses an asymmetric information with respect to the traditional one. We analyze it via the Russo-Vallois forward stochastic integral, i. e. using anticipating stochastic calculus, along with a white noise approach. We explicitly compute the optimal portfolios that maximize the expected logarithmic utility assuming different classical financial models: Black-Scholes-Merton, Heston, Vasicek. Similar results hold for other well-known models, such as the Hull-White and the Cox-Ingersoll-Ross ones. Our comparison between the performance of the traditional trader and the insider, although only asymmetrically informed, reveals that the privileged information overcompensates the delay in all cases, provided only one information flow is delayed. However, when two information flows are delayed, a competition between future information and delay magnitude enters into play, implying that the best performance depends on the parameter values. This, in turn, allows us to value future information in terms of time, and not only utility.

q-fin.MF↗

arXiv2024

Chemical Kinetics, Markov Chains, and the Imaginary Itô Interpretation

The abstract chemical reaction $$ A+A \to \emptyset, $$ understood as a Markov chain in continuous time, has been studied in the physical literature for several years. It has been claimed that this reaction can be described by means of the stochastic differential equation $$ d ϕ= - ϕ^2 dt + i \, ϕ\, dW_t, $$ where $i$ is the imaginary unit. This affirmation is, at least, intriguing, and has led to controversy and criticisms in the literature. The goal of this work is to give partial evidence that such a description may be possible.

math.PR↗

arXiv2023

Explicit blowing up solutions for a higher order parabolic equation with Hessian nonlinearity

In this work we consider a nonlinear parabolic higher order partial differential equation that has been proposed as a model for epitaxial growth. This equation possesses both global-in-time solutions and solutions that blow up in finite time, for which this blow-up is mediated by its Hessian nonlinearity. Herein, we further analyze its blow-up behaviour by means of the construction of explicit solutions in the square, the disc, and the plane. Some of these solutions show complete blow-up in either finite or infinite time. Finally, we refine a blow-up criterium that was proved for this evolution equation. Still, existent blow-up criteria based on a priori estimates do not completely reflect the singular character of these explicit blowing up solutions.

math.AP↗

arXiv2022

Chances for the honest in honest versus insider trading

We study a Black-Scholes market with a finite time horizon and two investors: an honest and an insider trader. We analyze it with anticipating stochastic calculus in two steps. First, we recover the classical result on portfolio optimization that shows that the expected logarithmic utility of the insider is strictly greater than that of the honest trader. Then, we prove that, whenever the market is viable, the honest trader can get a higher logarithmic utility, and therefore more wealth, than the insider with a strictly positive probability. Our proof relies on the analysis of a sort of forward integral variant of the Doléans-Dade exponential process. The main financial conclusion is that the logarithmic utility is perhaps too conservative for some insiders.

math.PR↗

arXiv2022

Itô versus Stratonovich in a stochastic cosmological model

In this work we study a stochastic version of the Friedmann acceleration equation. This model has been proposed in the cosmology literature as a possible explanation of the uncertainty found in the experimental quantification of the Hubble parameter. Its noise has been tacitly interpreted in the Stratonovich sense. Herein we prove that this interpretation leads to a positive probability of finite time blow-up of the solution, that is, of the Hubble parameter. In contrast, if we just modify the noise interpretation to that of Itô, then the solution globally exists almost surely. Moreover, the expected asymptotic behavior is found under this interpretation too.

math-ph↗

arXiv2021

A new method to detect globular clusters with the S-PLUS survey

In this paper, we describe a new method to select globular cluster (GC) candidates, including galaxy subtraction with unsharp masking, template fitting techniques and the inclusion of Gaia's proper motions. We report the use of the 12-band photometric system of S-PLUS to determine radial velocities and stellar populations of GCs around nearby galaxies. Specifically, we assess the effectiveness of identifying GCs around nearby and massive galaxies (D $< 20$ Mpc and $σ> 200$ km/s) in a multi-band survey such as S-PLUS by using spectroscopically confirmed GCs and literature GC candidate lists around the bright central galaxy in the Fornax cluster, NGC 1399 (D = 19 Mpc), and the isolated lenticular galaxy NGC 3115 (D = 9.4 Mpc). Despite the shallow survey depth, that limits the present work to $r < 21.3$ mag, we measure reliable photometry and perform robust SED fitting for a sample of 115 GCs around NGC 1399 and 42 GCs around NGC 3115, recovering radial velocities, ages, and metallicities for the GC populations.

astro-ph.GA↗

arXiv2021

Optimal portfolios for different anticipating integrals under insider information

We consider the non-adapted version of a simple problem of portfolio optimization in a financial market that results from the presence of insider information. We analyze it via anticipating stochastic calculus and compare the results obtained by means of the Russo-Vallois forward, the Ayed-Kuo, and the Hitsuda-Skorokhod integrals. We compute the optimal portfolio for each of these cases with the aim of establishing a comparison between these integrals in order to clarify their potential use in this type of problem. Our results give a partial indication that, while the forward integral yields a portfolio that is financially meaningful, the Ayed-Kuo and the Hitsuda-Skorokhod integrals do not provide an appropriate investment strategy for this problem.

math.PR↗

arXiv2021

Fluctuation-dissipation relation, Maxwell-Boltzmann statistics, equipartition theorem, and stochastic calculus

We derive the fluctuation-dissipation relation and explore its connection with the equipartition theorem and Maxwell-Boltzmann statistics through the use of different stochastic analytical techniques. Our first approach is the theory of backward stochastic differential equations, which arises naturally in this context, and facilitates the understanding of the interplay between these classical results of statistical mechanics. The second approach consists in deriving forward stochastic differential equations for the energy of an electric system according to both Itô and Stratonovich stochastic calculus rules. While the Itô equation possesses a unique solution, which is the physically relevant one, the Stratonovich equation admits this solution along with infinitely many more, none of which has a physical nature. Despite of this fact, some, but not all of them, obey the fluctuation-dissipation relation.

math.PR↗

arXiv2020

Kinetic energy of the Langevin particle

We compute the kinetic energy of the Langevin particle using different approaches. We build stochastic differential equations that describe this physical quantity based on both the Itô and Stratonovich stochastic integrals. It is shown that the Itô equation possesses a unique solution whereas the Stratonovich one possesses infinitely many, all but one absent of physical meaning. We discuss how this fact matches with the existent discussion on the Itô vs Stratonovich dilemma and the apparent preference towards the Stratonovich interpretation in the physical literature.

math.PR↗

arXiv2020

Reddening-free Q indices to identify Be star candidates

Astronomical databases currently provide high-volume spectroscopic and photometric data. While spectroscopic data is better suited to the analysis of many astronomical objects, photometric data is relatively easier to obtain due to shorter telescope usage time. Therefore, there is a growing need to use photometric information to automatically identify objects for further detailed studies, specially Hα emission line stars such as Be stars. Photometric color-color diagrams (CCDs) are commonly used to identify this kind of objects. However, their identification in CCDs is further complicated by the reddening effect caused by both the circumstellar and interstellar gas. This effect prevents the generalization of candidate identification systems. Therefore, in this work we evaluate the use of neural networks to identify Be star candidates from a set of OB-type stars. The networks are trained using a labeled subset of the VPHAS+ and 2MASS databases, with filters u, g, r, Hα, i, J, H, and K. In order to avoid the reddening effect, we propose and evaluate the use of reddening-free Q indices to enhance the generalization of the model to other databases and objects. To test the validity of the approach, we manually labeled a subset of the database, and use it to evaluate candidate identification models. We also labeled an independent dataset for cross dataset evaluation. We evaluate the recall of the models at a 99% precision level on both test sets. Our results show that the proposed features provide a significant improvement over the original filter magnitudes.

astro-ph.SR↗

arXiv2019

Water-methanol solutions characterized by liquid $μ$-jet XPS and DFT; the methanol hydration case

The advent of liquid $μ$-jet setups as proposed by Faubel and Winter in conjunction with X-ray Photoemission Spectroscopy (XPS) has opened up a large variety of experimental possibilities in the field of atomic and molecular physics. In this study, we present first results from a synchrotron-based XPS core level and valence band electron spectroscopy study on water (10$^{-4}$M aqueous NaCl solution) as well as a water-methanol mixture using the newly commissioned ALBA liquid $μ$-jet setup. The experimental results are compared with simulations from density functional theory (DFT) regarding the electronic structure of single molecules, pure molecular clusters, and mixed clusters configurations as well as previous experimental studies. We give a detailed interpretation of the core level and valence band spectra for the vapour and liquid phases of both sample systems. The resulting overall picture gives insight into the water-methanol concentrations of the vapour and liquid phases as well as into the local electronic structure of the pertinent molecular clusters under consideration, with a special emphasis on methanol as the simplest amphiphilic molecule capable of creating hydrogen bonds.

physics.atm-clus↗