Related papers: Renormalization of random models: a review

Let $\mathscr{T}$ be the regularity structure associated with a given system of singular stochastic PDEs. The paracontrolled representation of the $\sf \Pi$ map provides a linear parametrization of the nonlinear space of admissible models…

In the present paper we develop the general theory of renormalization of some nonequilibrium diagram technique. This technique roughly is the Keldysh diagram technique. To develop our theory we have used the Bogoliubov -Parasiuk R -…

There is growing body of learning problems for which it is natural to organize the parameters into matrix, so as to appropriately regularize the parameters under some matrix norm (in order to impose some more sophisticated prior knowledge).…

This paper constructs a solvability theory for a system of stochastic partial differential equations. On account of the Kolmogorov continuity theorem, solutions are looked for in certain H\"older-type classes in which a random field is…

Point processes are stochastic models generating interacting points or events in time, space, etc. Among characteristics of these models, first-order intensity and conditional intensity functions are often considered. We focus on…

We consider the application of regularization by dimensional reduction to NLO corrections of hadronic processes. The general collinear singularity structure is discussed, the origin of the regularization-scheme dependence is identified and…

A reduction procedure for stochastic differential equations based on stochastic symmetries including Girsanov random transformations is proposed. In this setting, a new notion of reconstruction is given, involving the expectation values of…

This paper surveys and discusses recent work adapting partial differential equation (PDE) models to discrete structures.

These lecture notes grew out of a series of lectures given by the second named author in short courses in Toulouse, Matsumoto, and Darmstadt. The main aim is to explain some aspects of the theory of "Regularity structures" developed…

In this work we prove convergence of renormalised models in the framework of regularity structures [Hai14] for a wide class of variable coefficient singular SPDEs in their full subcritical regimes. In particular, we provide for the first…

The reconstruction of the parameter of the model by the measurement of the random variable depending on this parameter is one of the main tasks of statistics. In the paper the notion of the statistically dual distributions is introduced.…

In this paper, we study randomized methods for feedback design of uncertain systems. The first contribution is to derive the sample complexity of various constrained control problems. In particular, we show the key role played by the…

We improve the estimates of the subgraph probabilities in a random regular graph. Using the improved results, we further improve the limiting distribution of the number of triangles in random regular graphs.

This paper is a brief review of recent developments in random matrix theory. Two aspects are emphasized: the underlying role of integrable systems and the occurrence of the distribution functions of random matrix theory in diverse areas of…

In the past years, the phenomenon of fractional regularity has been addressed for a large class of linear and/or quasilinear differential operators, mostly, in terms of certain Besov spaces. As it turned out, for equations governed by the…

Building upon the rule-algebraic stochastic mechanics framework, we present new results on the relationship of stochastic rewriting systems described in terms of continuous-time Markov chains, their embedded discrete-time Markov chains and…

In this document, we make a round up of the theory of asymptotic normality of sums of associated random variables, in a coherent approach in view of further contributions for new researchers in the field. (Version 01)

We develop a random model for relation algebras. We prove some preliminary results and pose questions that lay out a new direction of research.

Comment on ``Boosting Algorithms: Regularization, Prediction and Model Fitting'' [arXiv:0804.2752]

Nonlinear systems with model uncertainty are often described by stochastic differential equations. Some techniques from random dynamical systems are discussed. They are relevant to better understanding of solution processes of stochastic…