International Seminar on SDEs and Related Topics

This online seminar takes place about every four weeks on Friday at

12:30 UTC	11:30 UTC during European daylight saving time (starting Mach 29)

12:30 noon	1:30 pm	2:30 pm	8:30 pm (7:30 pm after March 29)
London	Berlin, Paris	Helsinki	Beijing

Zoom link Meeting ID: 618 9100 7917

No registration required. To get an e-mail reminder before each event write to sde-seminar[at]jyu.fi.

Organisers

Stefan Ankirchner (FSU Jena, Germany)
Christian Bender (Saarland University, Germany)
Rainer Buckdahn (Universite de Bretagne Occidentale, France)
Dan Crisan (Imperial College London, UK)
Hannah Geiss (University of Jyväskylä, Finland)
Stefan Geiss (University of Jyväskylä, Finland)
Céline Labart (Université Savoie Mont-Blanc, France)
Juan Li (Shandong University, China)
Andreas Neuenkirch (University of Mannheim, Germany)
Shige Peng (Shandong University, China)
Adrien Richou (University of Bordeaux, France)

Schedule 2026 Spring

Jan 16, 2026

Mark Veraar Poster:

Slides Video (expires July 2026)
(TU Delft, Netherlands)

What is non-trace class noise?

Abstract: In this talk, I will present a new method for proving estimates for Gaussian noise. We focus on a specific type of colored noise that lies in the intermediate regime between trace class and space-time white noise. This work is motivated by the theory of critical spaces for SPDEs, which we are currently extending to the non-trace class setting. No prior background in SPDEs is required, as the subject serves primarily as motivation. This presentation is based on joint work with Fabian Germ and Antonio Agresti.

Feb 13, 2026

Alexandre Popier Poster:

Slides Video (expires August 2026)
(Le Mans Université, France)

Reflected SDEs in time dependent non smooth domains. Applications to PDEs with Neumann boundary conditions

Abstract: In this talk, I will present new results on reflected stochastic differential equations (SDEs) in time dependent non smooth domains and on related semi-linear partial differential equations (PDEs) with Neumann boundary conditions.

This topic has been extensively studied, notably in the case of time-independent or regular domains; we will review the existing literature. In our paper we consider the normal reflection when the domain depends on time, is not smooth with convex time-slices. The existence and uniqueness of the solution of the reflected SDE is obtained through a strong penalization approximation using a sequence of standard diffusions, together with an additional regularization of the domain by smooth time-dependent domains.

Then, we study the corresponding generalized backward SDEs and derive a Feynman–Kac representation of the solutions to PDEs with Neumann boundary conditions. We will highlight the difficulties arising from the lack of regularity of the domains, notably with regard to the total variation of the increasing process associated to the reflection.

This presentation is based on joint work with Manal Jakani.

Mar 13 , 2026

Marcel Nutz Poster:

Slides Video (expires September 2026)
(Columbia University, USA)

Quadratically Regularized Optimal Transport

Abstract: Entropic optimal transport—the optimal transport problem regularized by Kullback–Leibler divergence—is highly successful in statistical applications. Thanks to the smoothness of the entropic coupling, its sample complexity avoids the curse of dimensionality, and the strong concavity of the dual problem enables fast computation. The flip side is overspreading: the entropic coupling always has full support, whereas the unregularized coupling that it approximates is usually sparse, often even given by a map. Quadratic regularization is known to allow for sparse approximations but is often thought to suffer from the curse of dimensionality, as the couplings have limited differentiability and the dual is not strongly concave. We refute this conventional wisdom and show that the key empirical quantities converge at the parametric rate. Moreover, we describe the geometry of the dual problem and show that several natural algorithms converge linearly. (Based on joint work with Alberto Gonzalez-Sanz, Eustasio del Barrio, Stephan Eckstein, and Andres Riveros Valdevenito.)

Apr 17, 2026 11:30 UTC (daylight saving time)

Saïd Hamadène Poster:

Slides Video (expires October 2026)
(Le Mans Université, France)

The optimal switching problem with signed switching costs

Abstract: In this talk we discuss the optimal multiple modes switching problem in finite horizon when the costs associated with the changes of regimes do not have a constant sign. From the economic point of view, this corresponds to the framework where the change of modes generates subsidies. The problem is solved by means of probabilistic tools. The main assumption is the monotonicity of the switching costs. In the Markov setting, the associated HJB system of PDEs is also considered. We show the existence and uniqueness of the solution in viscosity sense. Switching problems get involved in energy markets, financial markets, cybersecurity fields, etc.
This is a joint work with B. ElAsri and M. Souheil (Agadir University).

May 22, 2026

Roxana Dumitrescu Poster:

Video (expires November 2026)
(ENSAE-CREST, Institut Polytechnique de Paris, France)

A new probabilistic approach for optimal-stopping MFG

Abstract: We propose a novel probabilistic formulation for mean field games of optimal stopping (MFG-OSs) in the presence of randomized strategies. We characterize the mean field equilibrium through a new class of BSDEs, termed McKean-Vlasov reflected backward stochastic differential equations (MKV-RBSDEs). An equilibrium is characterized by a quintuple $(X,Y,Z,A,L)$, where $L$ is an adapted, $[0,1]$-valued, non-increasing càdlàg process, representing a randomized stopping strategy. The optimality of the randomized stopping strategy is endogenized directly via two novel Skorokhod-type conditions. We establish the existence of equilibria by applying the Kakutani–Fan–Glicksberg fixed-point theorem to a set-valued best-response map. Under alternative monotonicity assumptions, we derive an existence result using Tarski's fixed-point theorem, and we provide a constructive proof of existence of maximal and minimal equilibria. Furthermore, we prove the uniqueness of the equilibrium under specific conditions. We also show that a mean field equilibrium induces an approximate Nash equilibrium for the associated $N$-player stopping game. Finally, we connect our probabilistic formulation to the analytical approach, which is characterized by a system of constrained partial differential equations (joint work with Andrea Cosso and Laura D'Andolfi).

Jun 12, 2026

Thaleia Zariphopoulou Poster:

Video (expires November 2026)
(The University of Texas at Austin, USA)

On the optimal portfolio choice problem with partial information and related mean field games with relative performance criteria

In this talk, I will present mean field games in portfolio management with relative performance criteria, in markets when the drift of the stock is not fully observable. These are MFG with common noise and unbounded controls in the drift and the volatility. Both the utility and the couplings are rather general, extending all works to date. Using elements from indifference valuation, I will introduce a wide class of solutions and construct the value of the game and the optimal processes in closed form. Important role plays the single agent problem without competition for which I will present a new solution approach.
(Joint work with P. Souganidis).

Schedule 2025 Autumn

Oct 17, 2025

Mateusz Kwaśnicki Poster:

Slides Video (expires April 2026)
(Wrocław University of Science and Technology) Boundary traces of diffusions

In 1958 Spitzer showed that the 1-D Cauchy process can be obtained from the paths of the reflected 2-D Brownian motion in the half-plane H by retaining only points on the boundary, and rescaling time. A decade later Molchanov and Ostrovski proved that all symmetric stable Lévy processes arise similarly as boundary traces of suitable reflected diffusions.

In PDEs, it is a classical result that the generator of the Cauchy process is the Dirichlet-to-Neumann map for the Laplacian in H. In 2008, Caffarelli and Silvestre generalised this by identifying the generator of the symmetric stable Lévy process with the Dirichlet-to-Neumann map corresponding to the generator of Molchanov–Ostrovski diffusion.

These results illustrate a general principle: the generator K of the boundary trace of a reflected diffusion with generator L often coincides with the Dirichlet-to-Neumann map for L. This idea has been explored further by Assing, Benjamini, Chen, Fukushima, Herman, Hsu, Kim, Kolsrud, Molchanov, Motoo, Nagasawa, Rohde, Sato, Song, Ueno, Vondraček, Ying, and others.

Caffarelli and Silvestre posed a natural question: which translation-invariant operators arise as Dirichlet-to-Neumann maps for elliptic operators in H? Probabilistically: which Lévy processes can be realised as boundary traces of reflected diffusions? An answer to the PDE version was given in my joint paper with Mucha [1] for symmetric operators (in arbitrary dimension), and extended in [2] to non-symmetric operators. However, the corresponding probabilistic result does not follow directly, known results on Dirichlet-to-Neumann maps and boundary traces are too restrictive. A full characterisation of Lévy processes that are traces of reflected diffusions in H was given in [3], using a variety of probabilistic tools. The corresponding result for isotropic Lévy processes in higher dimensions appeared in [4].
In my talk I will state the problem more rigorously, survey the literature, and outline the main results of [3] and [4].

References:
[1] M. Kwaśnicki, J. Mucha. “Extension technique for complete Bernstein functions of the Laplace operator.” J. Evol. Equ., vol. 18, no. 3, 2018, pp. 1341–1379.
[2] M. Kwaśnicki. “Harmonic extension technique for non-symmetric operators with completely monotone kernels.” Calc. Var. Partial Differ. Equ., vol. 61, no. 202, 2022, pp. 1–40.
[3] M. Kwaśnicki. “Boundary traces of shift-invariant diffusions in half-plane.” Ann. Inst. Henri Poincaré Probab. Statist., vol. 59, no. 1, 2023, pp. 411–436.
[4] M. Kwaśnicki. “Harmonic extension technique: probabilistic and analytic perspectives.” Unpublished lecture notes, arXiv:2409.19118.

Nov 07, 2025

Antti Kupiainen Poster:

Slides Video (expires May 2026)
(University of Helsinki)

Probabilistic Conformal Field Theory

Abstract: Quantum Field Theories (QFT) provide the basic theoretical framework for both high energy and condensed matter physics. A special role in QFT is played by Conformal Field Theories (CFT) which are believed to describe QFTs in the limits of small and large length scales. CFTs have special symmetries leading to a rich mathematical structure. However, a rigorous mathematical foundation for CFT is still lacking. In this talk I’ll discuss a probabilistic approach to two dimensional CFT based on Gaussian Free Field and Gaussian Multiplicative Chaos. I will explain how the probabilistic approach leads to construction and complete solution of Liouville CFT which plays a central role in the theory of random surfaces and how these constructions could be extended to other CFTs. No background in QFT is assumed

Dec 12, 2025

Giovanni Conforti Poster:

Slides Video (expires June 2026)
(University of Padua and Ecole Polytechnique)

Coupling methods in stochastic control

Abstract: Coupling methods are a fundamental tool to derive smoothing and ergodicity properties of Markov semigroups. Aim of this talk is to survey some recent progress on the development of the coupling method in the field of stochastic control. In particular, we will see how constructing suitable couplings between controlled processes and solutions to forward-backward stochastic differential equations (FBSDEs) allows to obtain uniform-in-time gradient and Hessian bounds for Hamilton-Jacobi-Bellman equations. These estimates enjoy various applications, ranging from the turnpike property in stochastic control to the convergence of scaling algorithms in entropic optimal transport. Some of these will be illustrated at the end of the talk.

International Seminar on SDEs and Related Topics

Zoom link Meeting ID: 618 9100 7917

Organisers

Schedule 2026 Autumn

Oct 16, 2026

Nov 13, 2026

Dec 11, 2026

Schedule 2027 Spring

Jan 15, 2027

Feb 19, 2027

Mar 19, 2027

Apr 16, 2027

May 14, 2027

Jun 11, 2027