Propagation of chaos: a review of models, methods and applications. I. Models and methods
LP Chaintron, A Diez - arxiv preprint arxiv:2203.00446, 2022 - arxiv.org
The notion of propagation of chaos for large systems of interacting particles originates in
statistical physics and has recently become a central notion in many areas of applied …
statistical physics and has recently become a central notion in many areas of applied …
Concepts of quantum non-Markovianity: A hierarchy
Markovian approximation is a widely-employed idea in descriptions of the dynamics of open
quantum systems (OQSs). Although it is usually claimed to be a concept inspired by …
quantum systems (OQSs). Although it is usually claimed to be a concept inspired by …
User's guide to the fractional Laplacian and the method of semigroups
The method of semigroups is a unifying, widely applicable, general technique to formulate
and analyze fundamental aspects of fractional powers of operators L and their regularity …
and analyze fundamental aspects of fractional powers of operators L and their regularity …
[كتاب][B] Integro-differential elliptic equations
X Fernández-Real, X Ros-Oton - 2024 - Springer
Progress in Mathematics is a series of books intended for professional mathematicians and
scientists, encompassing all areas of pure mathematics. This distinguished series, which …
scientists, encompassing all areas of pure mathematics. This distinguished series, which …
Hausdorff dimension, heavy tails, and generalization in neural networks
Despite its success in a wide range of applications, characterizing the generalization
properties of stochastic gradient descent (SGD) in non-convex deep learning problems is …
properties of stochastic gradient descent (SGD) in non-convex deep learning problems is …
Deep ReLU network expression rates for option prices in high-dimensional, exponential Lévy models
We study the expression rates of deep neural networks (DNNs for short) for option prices
written on baskets of d risky assets whose log-returns are modelled by a multivariate Lévy …
written on baskets of d risky assets whose log-returns are modelled by a multivariate Lévy …
Approximation of the invariant measure of stable SDEs by an Euler–Maruyama scheme
Abstract We propose two Euler–Maruyama (EM) type numerical schemes in order to
approximate the invariant measure of a stochastic differential equation (SDE) driven by an α …
approximate the invariant measure of a stochastic differential equation (SDE) driven by an α …
[كتاب][B] Mathematical finance
E Eberlein, J Kallsen - 2019 - Springer
Ernst Eberlein Jan Kallsen Page 1 Springer Finance Ernst Eberlein Jan Kallsen Mathematical
Finance Page 2 Springer Finance Editorial Board Marco Avellaneda Giovanni Barone-Adesi …
Finance Page 2 Springer Finance Editorial Board Marco Avellaneda Giovanni Barone-Adesi …
Randomized Hamiltonian Monte Carlo as scaling limit of the bouncy particle sampler and dimension-free convergence rates
The bouncy particle sampler is a Markov chain Monte Carlo method based on a
nonreversible piecewise deterministic Markov process. In this scheme, a particle explores …
nonreversible piecewise deterministic Markov process. In this scheme, a particle explores …
Fractional calculus, anomalous diffusion, and probability
Abstract Ideas from probability can be very useful to understand and motivate fractional
calculus models for anomalous diffusion. Fractional derivatives in space are related to long …
calculus models for anomalous diffusion. Fractional derivatives in space are related to long …