Results 11 to 20 of about 108 (105)

The stationary AKPZ equation: Logarithmic superdiffusivity

Communications on Pure and Applied Mathematics, Volume 76, Issue 11, Page 3044-3103, November 2023., 2023
Abstract We study the two‐dimensional Anisotropic KPZ equation (AKPZ) formally given by ∂tH=12ΔH+λ((∂1H)2−(∂2H)2)+ξ,$$\begin{equation*} \hspace*{3.4pc}\partial _t H=\frac{1}{2}\Delta H+\lambda ((\partial _1 H)^2-(\partial _2 H)^2)+\xi , \end{equation*}$$where ξ is a space‐time white noise and λ is a strictly positive constant.
Giuseppe Cannizzaro, Dirk Erhard, Fabio Toninelli   +2 more
wiley   +1 more source

Freezing limits for Calogero–Moser–Sutherland particle models

Studies in Applied Mathematics, Volume 151, Issue 4, Page 1230-1281, November 2023., 2023
Abstract One‐dimensional interacting particle models of Calogero–Moser–Sutherland type with N particles can be regarded as diffusion processes on suitable subsets of RN$\mathbb {R}^N$ like Weyl chambers and alcoves with second‐order differential operators as generators of the transition semigroups, where these operators are singular on the boundaries ...
Michael Voit
wiley   +1 more source

Central Limit Theorem for Linear Eigenvalue Statistics of Non‐Hermitian Random Matrices

Communications on Pure and Applied Mathematics, Volume 76, Issue 5, Page 946-1034, May 2023., 2023
Abstract We consider large non‐Hermitian random matrices X with complex, independent, identically distributed centred entries and show that the linear statistics of their eigenvalues are asymptotically Gaussian for test functions having derivatives. Previously this result was known only for a few special cases; either the test functions were required ...
Giorgio Cipolloni, László Erdős, Dominik Schröder   +2 more
wiley   +1 more source

Time regularity for generalized Mehler semigroups

Mathematische Nachrichten, Volume 295, Issue 11, Page 2223-2245, November 2022., 2022
Abstract We study continuity and Hölder continuity of t↦Ptf$t\mapsto P_tf$, where Pt$P_t$ is a generalized Mehler semigroup in Cb(X)$C_b(X)$, the space of the continuous and bounded functions from a Banach space X to R$\mathbb {R}$, and f∈Cb(X)$f\in C_b(X)$.
Alessandra Lunardi
wiley   +1 more source

Vector‐valued generalized Ornstein–Uhlenbeck processes: Properties and parameter estimation

Scandinavian Journal of Statistics, Volume 49, Issue 3, Page 992-1022, September 2022., 2022
Abstract Generalizations of the Ornstein–Uhlenbeck process defined through Langevin equations, such as fractional Ornstein–Uhlenbeck processes, have recently received a lot of attention. However, most of the literature focuses on the one‐dimensional case with Gaussian noise.
Marko Voutilainen, Lauri Viitasaari, Pauliina Ilmonen, Soledad Torres, Ciprian Tudor   +4 more
wiley   +1 more source

An infinite‐dimensional affine stochastic volatility model

Mathematical Finance, Volume 32, Issue 3, Page 878-906, July 2022., 2022
Abstract We introduce a flexible and tractable infinite‐dimensional stochastic volatility model. More specifically, we consider a Hilbert space valued Ornstein–Uhlenbeck‐type process, whose instantaneous covariance is given by a pure‐jump stochastic process taking values in the cone of positive self‐adjoint Hilbert–Schmidt operators.
Sonja Cox, Sven Karbach, Asma Khedher
wiley   +1 more source

Consistent time‐homogeneous modeling of SPX and VIX derivatives

Mathematical Finance, Volume 32, Issue 3, Page 907-940, July 2022., 2022
Abstract This paper shows how to recover a stochastic volatility model (SVM) from a market model of the VIX futures term structure. Market models have more flexibility for fitting of curves than do SVMs, and therefore are better suited for pricing VIX futures and VIX derivatives.
Andrew Papanicolaou
wiley   +1 more source

Higher‐Order Riesz Transforms in the Inverse Gaussian Setting and UMD Banach Spaces

Journal of Function Spaces, Volume 2021, Issue 1, 2021., 2021
In this paper, we study higher‐order Riesz transforms associated with the inverse Gaussian measure given by πn/2ex2dx on ℝn. We establish Lpℝn,ex2dx‐boundedness properties and obtain representations as principal values singular integrals for the higher‐order Riesz transforms.
Jorge J. Betancor, Lourdes Rodríguez-Mesa, Dumitru Motreanu   +2 more
wiley   +1 more source

Quantitative Fourth Moment Theorem of Functions on the Markov Triple and Orthogonal Polynomials

Journal of Function Spaces, Volume 2021, Issue 1, 2021., 2021
In this paper, we consider a quantitative fourth moment theorem for functions (random variables) defined on the Markov triple (E, μ, Γ), where μ is a probability measure and Γ is the carré du champ operator. A new technique is developed to derive the fourth moment bound in a normal approximation on the random variable of a general Markov diffusion ...
Yoon Tae Kim, Hyun Suk Park, Shanhe Wu
wiley   +1 more source

Identification of the Polaron Measure I: Fixed Coupling Regime and the Central Limit Theorem for Large Times

Communications on Pure and Applied Mathematics, Volume 73, Issue 2, Page 350-383, February 2020., 2020
Abstract We consider the Fröhlich model of the polaron, whose path integral formulation leads to the transformed path measurewith respect to ℙ that governs the law of the increments of the three‐dimensional Brownian motion on a finite interval [−T, T], and Zα, T is the partition function or the normalizing constant and α > 0 is a constant, or the ...
Chiranjib Mukherjee, S. R. S. Varadhan
wiley   +1 more source