{"id":20446,"date":"2026-04-29T19:16:48","date_gmt":"2026-04-29T17:16:48","guid":{"rendered":"https:\/\/scm.iec.cat\/?post_type=sessions&p=20446"},"modified":"2026-10-14T11:45:30","modified_gmt":"2026-10-14T09:45:30","slug":"bmd-2026-stochastic-analysis","status":"publish","type":"sessions","link":"https:\/\/scm.iec.cat\/eng\/sessions\/bmd-2026-stochastic-analysis\/","title":{"rendered":"BMD 2026 \u2013 Stochastic Analysis"},"content":{"rendered":"

GENERAL DESCRIPTION<\/strong><\/h3>\n

This thematic session brings together research groups from across Catalonia working in stochastic analysis, with a particular focus on topics closely related to those addressed in the plenary lecture by Dan Crisan. The session will showcase the rich interplay between stochastic analysis and a broad spectrum of mathematical disciplines, featuring talks on mathematical analysis, partial differential equations, financial mathematics, and climate modelling. It aims to foster scientific exchange and highlight recent advances at the interface of these research areas.<\/p>\n

____________________________________________________________________<\/p>\n

SCHEDULE<\/strong><\/h3>\n
Dijous 8 d’octubre (Nicolau d\u2019Olwer)<\/h5>\n

11:00h<\/strong> Explicit domain preserving integrators for a class of SDEs<\/em>,\u00a0David Cohen<\/strong> (Chalmers University of Technology, G\u00f6teborg)
\n11:40h <\/strong>Inference and Estimation in Second-Order Markov Multistate Models: Theory, Simulations, and Clinical Application, <\/em>Mireia Besal\u00f9<\/strong> (Universitat Polit\u00e8cnica de Catalunya)
\n12:20h<\/strong> Kac-Stroock type approximations for the Brownian motion<\/em>, Salim Boukfal<\/strong> (Universitat Aut\u00f2noma de Barcelona)<\/span><\/span><\/p>\n

 <\/p>\n

Divendres 9 d’octubre (Pi i Sunyer)<\/h5>\n

11:00h <\/strong>Takagi-Type Curves: SBR measure and Local<\/em> Time, by Frank Proske<\/strong> (University of Oslo)<\/span><\/span>
\n11:40h<\/strong> On the skew-curvature power law relationship in stochastic volatility models with L\u00e9vy jumps,<\/em> by <\/span>\u00d2scar Bur\u00e9s <\/strong>(Universitat de Barcelona)<\/span><\/span>
\n12:20h<\/strong> On counting processes,<\/em> Anthony R\u00e9veillac <\/strong>(Institut National de Sciences Appliqu\u00e9es, Toulouse)<\/span><\/span><\/p>\n

____________________________________________________________________<\/p>\n

ABSTRACTS<\/strong><\/h3>\n
Takagi-Type Curves: SBR measure and Local Time<\/strong><\/em>
\nby Frank Proske<\/strong> (University of Oslo)<\/span><\/span>
\n<\/span><\/h5>\n

Abstract<\/strong>
\nWe investigate occupation measures and local times of rough Takagi-type functions. By embedding these curves into a hyperbolic dynamical system related to the baker transformation, we establish a connection between SBR measures, Bernoulli convolutions and occupation measures. Using Fourier-analytic and equidistribution methods, we prove the existence of square-integrable local times for Takagi-type curves for specific ranges of the roughness parameter. The motivation for this work also comes from stochastic<\/span> regularization theory, where irregular perturbations can restore well-posedness of differential equations.<\/p>\n

References<\/p>\n

[1] K. Bara\u0144ski, B. B\u00e1r\u00e1ny, J. Romanowska. On the dimension of the graph of the classical Weierstrass function. Advances in Mathematics 265 (2014), 32\u201359.<\/p>\n

[2] P. Imkeller, O. Menoukeu Pamen, G. dos Reis, A. R\u00e9veillac. Rough Weierstrass functions and dynamical systems: the smoothness of the SBR measure. Pure and Applied Functional Analysis 7 (2022), 1273\u20131305.<\/p>\n

____________________________________________________________________<\/p>\n

Kac-Stroock type approximations for the Brownian motion<\/strong><\/em>
\nby Salim Boukfal (Universitat Aut\u00f2noma de Barcelona)<\/span><\/span><\/strong><\/h5>\n

Abstract<\/strong>
\nThis talk provides an overview of results concerning the weak approximation of Gaussian processes such as Brownian motion, its multiparameter analog, the Brownian sheet, and stochastic integrals with respect to such processes to finally see how these results can be applied to approximate the law of the solution to the stochastic Poisson equation. We mainly focus on approximations constructed from integrated random telegraph processes whose switching rates are described by a renewal process.<\/p>\n

____________________________________________________________________<\/p>\n

Explicit domain preserving integrators for a class of SDEs<\/strong><\/em>
\nby David Cohen<\/strong> (Chalmers University of Technology, G\u00f6teborg)<\/h5>\n

Abstract<\/strong>
\nWe propose and study explicit time integrators for SDEs having solutions in a hypercube.
\nWe provide strong and weak rates of convergence for these domain preserving integrators.
\nWe illustrate these results numerically.<\/p>\n

The talk is based on a joint work with Charles-Edouard Br\u00e9hier (Universit\u00e9 de Pau et des Pays de l\u2019Adour)<\/p>\n

____________________________________________________________________<\/p>\n

On the skew-curvature power law relationship in stochastic volatility models with L\u00e9vy jumps<\/strong><\/em>
\nby \u00d2scar Bur\u00e9s<\/strong> (Universitat de Barcelona)<\/span><\/h5>\n
\n

Abstract<\/strong>
\nThe short-term blow up behaviour of the ATM-IV skew is commonly modelled by either a rough volatility process with small Hurst index or an infinite variation L\u00e9vy process in the log-price dynamics. In this talk we examine which is the effect of mixed dynamics (i.e. rough volatility and infinite variation L\u00e9vy processes) on the ATM-IV skew and curvature. The results show that the analysis of the leading terms of the short-time expansion of both ATM-IV skew and curvature allow us to determine, from a mixed dynamics model, which mechanism originated the power-law behaviour on the skew and on the curvature. Apart from showing that the mixed model also originates a power law, the results have also key implications in model design and calibration.<\/p>\n<\/div>\n

____________________________________________________________________<\/h5>\n
\n
On counting processes,<\/strong><\/em>
\nby <\/strong>Anthony R\u00e9veillac (Institut National de Sciences Appliqu\u00e9es, Toulouse)<\/strong><\/h5>\n

 <\/p>\n<\/div>\n

\n

Abstract<\/strong>
\nMotivated by question in Cyber Risk Insurance modelling, we investigate some general structure on counting processes. Indeed, we are interested on how one can capture inner dependence structure of random events and like the notion of cluster in case of contagion-type phenomena. We address this question using Malliavin\u2019s calculus type tools in line with recent developments we produced in this direction. This talk is based on a joint work with C. Hillairet, T. Peyrat and A. Pommier.\u00bb<\/p>\n<\/div>\n

____________________________________________________________________<\/h5>\n
Inference and Estimation in Second-Order Markov Multistate Models: Theory, Simulations, and Clinical Application<\/em><\/strong>
\nby Mireia Besal\u00fa<\/strong> (Universitat Polit\u00e8cnica de Catalunya)<\/h5>\n

Abstract
\n<\/strong>Multistate models are widely applied to describe the clinical course of a disease and to model the progression of patients among various health states. Standard methodologies rely on the first-order Markov assumption, where the future evolution of the stochastic process only depends on the current state and often fails in complex clinical scenarios. To address this limitation, we extend the traditional framework by relaxing this assumption to a second-order Markov process, where future state transitions depend on both the current and immediate past states.<\/p>\n

To overcome the high-dimensional estimation challenges inherent to higher-order transitions, we utilize state-specific extended transition probability matrices and generalize the Chapman-Kolmogorov equations for $n$-step second-order probabilities.<\/p>\n

In this work, we propose two consistent, non-parametric estimators under time-homogeneity for these transition probabilities: a direct ratio of conditional transitions to individuals at risk, and an averaged estimator based on time-specific conditional probabilities. We establish their asymptotic properties and derive explicit variance formulas.<\/p>\n

Finally, we demonstrate the utility of our framework using a cohort of over 3,000 hospitalized COVID-19 patients in Barcelona. The multistate model captures 14 possible transitions among seven distinct post-admission states.We have observed possible differences in patient progression to non-invasive and invasive mechanical ventilation based on initial pneumonia severity, differences that would not be detectable under a first-order Markov assumption.<\/p>\n

This is a joint work with Josu Najera-Zuloaga and Guadalupe G\u00f3mez Melis.<\/p>\n","protected":false},"parent":0,"template":"","categoria_sessions_conferences":[238],"class_list":["post-20446","sessions","type-sessions","status-publish","hentry","categoria_sessions_conferences-bmd-2026"],"acf":[],"_links":{"self":[{"href":"https:\/\/scm.iec.cat\/eng\/wp-json\/wp\/v2\/sessions\/20446","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/scm.iec.cat\/eng\/wp-json\/wp\/v2\/sessions"}],"about":[{"href":"https:\/\/scm.iec.cat\/eng\/wp-json\/wp\/v2\/types\/sessions"}],"wp:attachment":[{"href":"https:\/\/scm.iec.cat\/eng\/wp-json\/wp\/v2\/media?parent=20446"}],"wp:term":[{"taxonomy":"categoria_sessions_conferences","embeddable":true,"href":"https:\/\/scm.iec.cat\/eng\/wp-json\/wp\/v2\/categoria_sessions_conferences?post=20446"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}