Results 31 to 40 of about 3,983,040 (155)

Martingale Hardy spaces with variable exponents [PDF]

Banach Journal of Mathematical Analysis, 2016
In this paper, we introduce Hardy spaces with variable exponents defined on a probability space and develop the martingale theory of variable Hardy spaces. We prove the weak type and strong type inequalities on Doob's maximal operator and get a $(1,p(\cdot),\infty)$-atomic decomposition for Hardy martingale spaces associated with conditional square ...
Jiao, Yong, Zhou, Dejian, Hao, Zhiwei, Chen, Wei   +3 more
openaire   +3 more sources

Conformally invariant random fields, Liouville quantum gravity measures, and random Paneitz operators on Riemannian manifolds of even dimension

Journal of the London Mathematical Society, Volume 110, Issue 5, November 2024.
Abstract For large classes of even‐dimensional Riemannian manifolds (M,g)$(M,g)$, we construct and analyze conformally invariant random fields. These centered Gaussian fields h=hg$h=h_g$, called co‐polyharmonic Gaussian fields, are characterized by their covariance kernels k which exhibit a precise logarithmic divergence: |k(x,y)−log1d(x,y)|≤C$\big ...
Lorenzo Dello Schiavo, Ronan Herry, Eva Kopfer, Karl‐Theodor Sturm   +3 more
wiley   +1 more source

Reference dependence and endogenous anchors

Mathematical Finance, Volume 34, Issue 3, Page 925-976, July 2024.
Abstract In a complete market, we find optimal portfolios for an investor whose satisfaction stems from both a payoff's intrinsic utility and its comparison with an endogenous reference as modeled by Kőszegi and Rabin. In the regular regime, arising when reference dependence is low, the marginal utility of the optimal payoff is proportional to a twist ...
Paolo Guasoni, Andrea Meireles‐Rodrigues   +1 more
wiley   +1 more source

On noncommutative distributional Khintchine type inequalities

Bulletin of the London Mathematical Society, Volume 56, Issue 7, Page 2278-2295, July 2024.
Abstract The purpose of this paper is to provide distributional estimates for the series of the form ∑k=1∞xk⊗rk$\sum _{k=1}^\infty x_k\otimes r_k$ with {xk}k⩾1$\lbrace x_k\rbrace _{k\geqslant 1}$ being elements from noncommutative Lorentz spaces Λlog1/2(M)$\Lambda _{\log ^{1/2}}(\mathcal {M})$ and {rk}k⩾1$\lbrace r_k\rbrace _{k\geqslant 1}$ being ...
Yong Jiao, Xingyan Quan, Fedor Sukochev, Dmitriy Zanin   +3 more
wiley   +1 more source

Branching random walk with non‐local competition

Journal of the London Mathematical Society, Volume 109, Issue 6, June 2024.
Abstract We study the Bolker–Pacala–Dieckmann–Law (BPDL) model of population dynamics in the regime of large population density. The BPDL model is a particle system in which particles reproduce, move randomly in space and compete with each other locally.
Pascal Maillard, Sarah Penington
wiley   +1 more source

Well‐posedness of stochastic heat equation with distributional drift and skew stochastic heat equation

Communications on Pure and Applied Mathematics, Volume 77, Issue 5, Page 2708-2777, May 2024.
Abstract We study stochastic reaction–diffusion equation ∂tut(x)=12∂xx2ut(x)+b(ut(x))+Ẇt(x),t>0,x∈D$$\begin{equation*} \partial _tu_t(x)=\frac{1}{2} \partial ^2_{xx}u_t(x)+b(u_t(x))+\dot{W}_{t}(x), \quad t>0,\, x\in {D} \end{equation*}$$where b$b$ is a generalized function in the Besov space Bq,∞β(R)$\mathcal {B}^\beta _{q,\infty }(\mathbb {R})$, D⊂R${
Siva Athreya, Oleg Butkovsky, Khoa Lê, Leonid Mytnik   +3 more
wiley   +1 more source

Testing the martingale difference hypothesis using integrated regression functions [PDF]

, 2006
An omnibus test for testing a generalized version of the martingale difference hypothesis (MDH) is proposed. This generalized hypothesis includes the usual MDH, testing for conditional moments constancy such as conditional homoscedasticity (ARCH effects)
Velasco Gómez, Carlos, Carlos Velasco, Escanciano, J.C. (Juan Carlos), Velasco, C. (Carlos), J. Carlos Escanciano, Velasco, Carlos, Escanciano, Juan Carlos   +6 more
core   +1 more source

Designing universal causal deep learning models: The geometric (Hyper)transformer

Mathematical Finance, Volume 34, Issue 2, Page 671-735, April 2024.
Abstract Several problems in stochastic analysis are defined through their geometry, and preserving that geometric structure is essential to generating meaningful predictions. Nevertheless, how to design principled deep learning (DL) models capable of encoding these geometric structures remains largely unknown.
Beatrice Acciaio, Anastasis Kratsios, Gudmund Pammer   +2 more
wiley   +1 more source

Hardy Spaces of 2-Parameter Brownian Martingales

Tokyo Journal of Mathematics, 1985
We investigate 2-parameter Brownian martingales and give some applications to Hardy spaces on the torus. In order to describe our results we prepare notations: Let \(T^ 2\) be the distinguished boundary of the bidisc. Let \({\mathcal H}^ 1(T^ 2)\) (resp.
openaire   +3 more sources

Linear Functionals on Certain Martingale Hardy Spaces.

Interdisciplinary Information Sciences, 1998
The author introduces some Hardy spaces associated with a rearrangement invariant Banach function space and containing all càdlàg processes, all adapted càdlàg processes and all martingales, respectively. The duals of these Hardy spaces are characterized and so some duality results from the books of \textit{A. M.
openaire   +2 more sources