Frontiers in Stochastic Analysis–BSDEs, SPDEs and their Applications, Edinburgh, July 2017. Selected, Revised and Extended Contributions

doi:10.1007/978-3-030-22285-7

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Frontiers in Stochastic Analysis–BSDEs, SPDEs and their Applications, Edinburgh, July 2017. Selected, Revised and Extended Contributions

Springer, 2019.

Academic editor: S. Cohen, I. Gyöngy, G. dos Reis, D. Šiška, L. Szpruch

This collection of selected, revised and extended contributions resulted from a Workshop on BSDEs, SPDEs and their Applications that took place in Edinburgh, Scotland, July 2017 and included the 8th World Symposium on BSDEs.

The volume addresses recent advances involving backward stochastic differential equations (BSDEs) and stochastic partial differential equations (SPDEs). These equations are of fundamental importance in modelling of biological, physical and economic systems, and underpin many problems in control of random systems, mathematical finance, stochastic filtering and data assimilation. The papers in this volume seek to understand these equations, and to use them to build our understanding in other areas of mathematics.

This volume will be of interest to those working at the forefront of modern probability theory, both established researchers and graduate students.

On the Wellposedness of Some McKean Models with Moderated or Singular Diffusion Coefficient

Jabir J. M., Bossy M., , in: Frontiers in Stochastic Analysis–BSDEs, SPDEs and their Applications, Edinburgh, July 2017. Selected, Revised and Extended Contributions.: Springer, 2019. Ch. 2 P. 43–87.

We investigate the well-posedness problem related to two models of nonlinear McKean Stochastic Differential Equations with some local interaction in the diffusion term. First, we revisit the case of the McKean-Vlasov dynamics with moderate interaction, previously studied by Méléard and Jourdain in [16], under slightly weaker assumptions, by showing the existence and uniqueness of a ...

Added: September 24, 2020

Priority areas: mathematics

Language: English

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Keywords: mathematical finance Stochastic control SPDEs McKean-Vlasov models BSDEs World Symposium

Frontiers in Stochastic Analysis–BSDEs, SPDEs and their Applications, Edinburgh, July 2017. Selected, Revised and Extended Contributions

Bifurcations and Structural Stability of Generic PC-HC Families

Dorovskiy A., / Series arXiv "math". 2026.

In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...

Added: May 14, 2026

On the minimum number of maximal distance-k independent sets in trees

Taletskii D., / Series arXiv "math". 2026.

A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...

Added: May 1, 2026

On Arithmetic Mirror Symmetry for smooth Fano fourfolds

Ovcharenko M., / Series arXiv "math". 2026.

We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n⩽4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, ...

Added: April 30, 2026

On weak solutions to the 1d compressible Navier-Stokes equations: a Lipschitz continuous dependence on data in weaker norms and an error of their homogenization

Zlotnik Alexander, / Series arXiv "math". 2026. No. 2602.03481v1.

We deal with the global in time weak solutions to the 1D compressible Navier-Stokes system of equations for large discontinuous initial data and nonhomogeneous boundary conditions of three standard types. We prove the Lipschitz-type continuous dependence of the solution $(\eta,u,\theta)$, in a norm slightly stronger than $L^{2,\infty}(Q)\times L^2(Q)\times L^2(Q)$, on the initial data $(\eta^0,u^0,e^0)$ in a ...

Added: April 18, 2026

On the dimension of the space of static potentials on three-manifolds

Medvedev V., / Series arXiv "math". 2026.

We investigate the interplay between the dimension of the space of static potentials and the geometric and topological structure of the underlying static three-manifold. A partial classification of boundaryless static manifolds is obtained in terms of this dimension. We also treat the case of static manifolds with boundary. In particular, we prove that if a ...

Added: April 3, 2026

Using predefined vector systems to speed up neural network multimillion class classification

Gabdullin N., Androsov I., / Series Computer Science "arxiv.org". 2026.

Label prediction in neural networks (NNs) has O(n) complexity proportional to the number of classes. This holds true for classification using fully connected layers and cosine similarity with some set of class prototypes. In this paper we show that if NN latent space (LS) geometry is known and possesses specific properties, label prediction complexity can ...

Added: April 2, 2026

Homogeneous maximizers of the Blaschke-Santalo-type functionals

Kolesnikov A., / Series arXiv "math". 2025.

We study Blaschke--Santal{ó}-type inequalities for N>=2 sets (functions) and a special class of cost functions. In particular, we prove new results about reduction of the maximization problem for the Blaschke--Santal{ó}-type functional to homogeneous case (functional inequalities on the sphere) and extend the symmetrization argument to the case of N>2 sets. We also discuss links to the ...

Added: February 13, 2026

Iterative Ricci-Foster Curvature Flow with GMM-Based Edge Pruning: A Novel Approach to Community Detection

Sorokin K., Beketov M., Онучин А. et al., / arxiv.org. Серия cs.SI "Social and Information Networks ". 2025.

Community detection in complex networks is a fundamental problem, open to new approaches in various scientific settings. We introduce a novel community detection method, based on Ricci flow on graphs. Our technique iteratively updates edge weights (their metric lengths) according to their (combinatorial) Foster version of Ricci curvature computed from effective resistance distance between the ...

Added: January 15, 2026

On finding formal power-logarithmic expansions of solutions to q-difference equations

Gaianov N., Parusnikova A., / Cornell University. Серия math "arxiv.org". 2025.

An algebraic q-difference equation is considered. A sufficient condition for the existence of a formal power-logarithmic expansion of a solution to such an equation in the neighborhood of zero is proposed. An example of applying this sufficient condition for constructing a formal expansion of a solution to a certain q-difference analogue of the fifth Painlevé equation ...

Added: December 25, 2025

Ideal of the variety of flexes of plane cubics

Popov V., / Series arXiv "math". 2025. No. 2502.01539.

We prove that the variety of flexes of algebraic curves of degree 3 in the projective plane is an ideal theoretic complete intersection in the product of a two-dimensional and a nine-dimensional projective spaces. ...

Added: December 16, 2025

Random walks on rank one symmetric spaces of noncompact type

Gnetov F., Konakov V., / Series arXiv "math". 2025. No. 2512.04667.

We establish a central limit theorem, a local limit theorem, and a law of large numbers for a natural random walk on a symmetric space M of non-compact type and rank one. This class of spaces, which includes the complex and quaternionic hyperbolic spaces and the Cayley hyperbolic plane, generalizes the real hyperbolic space Hn. Our approach introduces ...

Added: December 5, 2025

Cascades of Lorenz attractors in the Shimizu-Morioka model

Kazakov A., Koryakin V., Safonov K. et al., / Series arXiv "math". 2025.

The Lorenz attractor is the first example of a robustly chaotic non-hyperbolic attractor. Each orbit of such an attractor has a positive top Lyapunov exponent, and this property persists under small perturbations despite possible bifurcations of the attractor. In this paper, we study the boundary of the Lorenz attractor existence region in the Shimizu-Morioka model. ...

Added: December 4, 2025

Асимптотический вариант метода параметрикс для цепей Маркова, сходящихся к диффузиям

Bitter I., Konakov V., / Cornell University. Серия arXiv "math". 2025. № 2505.24548.

В работе приводится обобщение локальной предельной теоремы о сходимости неоднородных цепей Маркова к диффузионному пределу на случай, когда соответ- ствующие коэффициенты процессов удовлетворяют слабым условиям регулярности и совпадают лишь асимптотически. В частности, рассматриваемые нами коэффици- енты сноса могут быть неограниченными с не более чем линейным ростом, а оценки отражают перенос терминального состояния неограниченным трендом через ...

Added: December 3, 2025

Stabilization of direct images for curves

Bogomolov F. A., Schrandt S., / Series arXiv "math". 2025.

We discuss phenomena of stabilization for direct images of line bundles over projective curves mapping onto the projective line, for maps of sufficiently big degree. ...

Added: December 1, 2025

Upper Bounds on the Torsion Index of Half-Spin Groups

Deviatov R., Baek S., / Series arXiv "math". 2025.

The torsion index of split simple groups has been extensively studied, notably by Totaro, who calculated the torsion indexes of the spin groups and $E_{8}$ in [5] and [6], respectively. The aim of this paper is to provide upper bounds for the torsion index of half-spin groups, the only remaining case in the calculation of ...

Added: December 1, 2025

Hessian-based lightweight neural network for brain vessel segmentation on a minimal training dataset

Меньшиков И. А., Бернадотт А. К., Elvimov N. S., / Series arXie "Statistical mechanics". 2025.

Accurate segmentation of blood vessels in brain magnetic resonance angiography (MRA) is essential for successful surgical procedures, such as aneurysm repair or bypass surgery. Currently, annotation is primarily performed through manual segmentation or classical methods, such as the Frangi filter, which often lack sufficient accuracy. Neural networks have emerged as powerful tools for medical image ...

Added: December 1, 2025

Birational transformations of threefold Q-conic bundles

Prokhorov Y., / Series arXiv "math". 2025.

A $\mathbf{Q}$-conic bundle is a contraction $f: X\to Z$ of a three-dimensional algebraic variety $X$ to a surface~$Z$ such that the variety~$X$ has only terminal $\mathbf{Q}$-factorial singularities, the anticanonical divisor $-K_X$ is~$f$-ample, and $\uprho(X/Z)=1$. We provide an algorithm to transform a $\mathbf{Q}$-conic bundle to its standard form. ...

Added: December 1, 2025

Birational geometry of hyperkahler manifolds and the Hu-Yau conjecture

Amerik E., Verbitsky M., Soldatenkov A., / Series arXiv "math". 2025.

Wierzba and Wisniewski proved that in dimension 4, every bimeromorphic map of hyperkahler manifolds is represented as a composition of Mukai flops. Hu and Yau conjectured that this result can be generalized to arbitrary dimension. They defined ``Mukai's elementary transformation'' as the blow-up of a subvariety ruled by complex projective spaces, composed with the contraction ...

Added: December 1, 2025

Automorphisms of bounded growth

Kuznetsova A., / Series arXiv "math". 2025.

We study birational automorphisms of algebraic varieties of bounded growth, i.e. such that the norms of the inverse images ${(f^n)}^* \colon \mathrm{NS}(X)\to \mathrm{NS}(X)$ of the powers of the automorphism $f\in\mathrm{Bir}(X)$ are bounded above for $n\geqslant 0$. We prove that some power of an infinite order automorphism of a variety $X$ with such property factors either ...

Added: December 1, 2025

On the Wellposedness of Some McKean Models with Moderated or Singular Diffusion Coefficient

Added: September 24, 2020

Non-iterative Solution to Robust Anisotropy-based Analysis and Control Problems for Uncertain Descriptor Systems

Andrianova O., Белов А. А., , in: 2019 23rd International Conference on System Theory, Control and Computing (ICSTCC).: IEEE, 2019. P. 455–460.

The problem of robust admissibilization with guaranteed random disturbance attenuation level for discrete-time time-invariant (LDTI) descriptor systems with norm-bounded uncertainties is considered. The input disturbance is supposed to be a stationary Gaussian sequence with bounded mean anisotropy level. The solutions to analysis and robust statefeedback control problems are formulated in terms of matrix inequalities. The obtained conditions are convex over ...

Added: December 5, 2019

Periodic strategies in optimal execution with multiplicative price impact

Hernández-Hernández D., Moreno-Franco H. A., Pérez J., Mathematical Finance 2019 Vol. 29 No. 4 P. 1039–1065

We study the optimal execution problem with multiplicative price impact in algorithmic trading, when an agent holds an initial position of shares of a financial asset. The interselling decision times are modeled by the arrival times of a Poisson process. The criterion to be optimized consists in maximizing the expected net present value of the gains of ...

Added: May 2, 2017

Solution to HJB equations with an elliptic integro-differential operator and gradient constraint

Moreno-Franco H. A., Applied Mathematics and Optimization 2018 Vol. 78 No. 1 P. 25–60

The main goal of this paper is to establish existence, regularity and uniqueness results for the solution of a Hamilton–Jacobi–Bellman (HJB) equation, whose operator is an elliptic integro-differential operator. The HJB equation studied in this work arises in singular stochastic control problems where the state process is a controlled d-dimensional Lévy process. ...

Added: October 12, 2016