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
PR Stinga - Handbook of fractional calculus with applications, 2019 - degruyter.com
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 …
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
P Chen, CS Deng, RL Schilling, L Xu - Stochastic Processes and their …, 2023 - Elsevier
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 …
[图书][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
G Deligiannidis, D Paulin… - The Annals of Applied …, 2021 - projecteuclid.org
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
MM Meerschaert - Fractional dynamics: recent advances, 2012 - World Scientific
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 …
Periodic homogenization of nonlocal operators with a convolution-type kernel
A Piatnitski, E Zhizhina - SIAM Journal on Mathematical Analysis, 2017 - SIAM
The paper deals with a homogenization problem for a nonlocal linear operator with a kernel
of convolution type in a medium with a periodic structure. We consider the natural diffusive …
of convolution type in a medium with a periodic structure. We consider the natural diffusive …