Results 21 to 30 of about 108 (105)

Long Term Behavior for a Class of Stochastic Delay Lattice Systems in Xρ Space

Discrete Dynamics in Nature and Society, Volume 2020, Issue 1, 2020., 2020
In this paper, we focus on the asymptotic behavior of solutions to stochastic delay lattice equations with additive noise and deterministic forcing. We first show the existence of a continuous random dynamical system for the equations. Then we investigate the pullback asymptotical compactness of solutions as well as the existence and uniqueness of ...
Yijin Zhang, Zongbing Lin, Douglas R. Anderson   +2 more
wiley   +1 more source

Symmetric Ornstein-Uhlenbeck semigroups and their generators

Probability Theory and Related Fields, 2002
We provide necessary and sufficient conditions for a Hilbert space-valued Ornstein-Uhlenbeck process to be reversible with respect to its invariant measure $ $. For a reversible process the domain of its generator in $L^p( )$ is characterized in terms of appropriate Sobolev spaces thus extending the Meyer equivalence of norms to any symmetric ...
Chojnowska-Michalik, Anna, Goldys, Beniamin   +1 more
openaire   +3 more sources

Analysis of Operators with Complex Gaussian Kernels over ${\mathcal{ℰ}}^{\prime }$(ℝ): Abelian Theorems

Axioms
This paper investigates Abelian theorems for operators with complex Gaussian kernels over distributions of compact support. Furthermore, our investigation encompasses an examination of the Gauss–Weierstrass semigroup, the linear canonical transform, and ...
Hari M. Srivastava, Emilio R. Negrín, Jeetendrasingh Maan   +2 more
doaj   +1 more source

Harnack Inequalities and Applications for Ornstein–Uhlenbeck Semigroups with Jump [PDF]

Potential Analysis, 2011
The Harnack inequality established in [13] for generalized Mehler semigroup is improved and generalized. As applications, the log-Harnack inequality, the strong Feller property, the hyper-bounded property, and some heat kernel inequalities are presented for a class of O-U type semigroups with jump. These inequalities and semigroup properties are indeed
Ouyang, Shun-Xiang, Röckner, Michael, Wang, Feng-Yu   +2 more
openaire   +6 more sources

Brownian Motion With Partial Resetting Conditioned to Stay Positive

Bulletin of the London Mathematical Society, Volume 58, Issue 3, March 2026.
Abstract We consider Brownian motion with partial resetting, which has recently attracted a lot of attention in physics as well as the mathematics literature. We analyze the speed of convergence of this process towards stationarity as well as its quasistationary behavior.
Martin Kolb, Achim Wübker
wiley   +1 more source

Non-Differentiable Skew Convolution Semigroups and Related Ornstein–Uhlenbeck Processes [PDF]

Potential Analysis, 2004
It is proved that a general non-differentiable skew convolution semigroup associated with a strongly continuous semigroup of linear operators on a real separable Hilbert space can be extended to a differentiable one on the entrance space of the linear semigroup.
Dawson, Donald A., Li, Zenghu
openaire   +3 more sources

Dynamically Consistent Analysis of Realized Covariations in Term Structure Models

Mathematical Finance, Volume 36, Issue 1, Page 203-236, January 2026.
ABSTRACT In this article, we show how to analyze the covariation of bond prices nonparametrically and robustly, staying consistent with a general no‐arbitrage setting. This is, in particular, motivated by the problem of identifying the number of statistically relevant factors in the bond market under minimal conditions.
Dennis Schroers
wiley   +1 more source

A Variational Formulation of European Option Prices in the 1‐Hypergeometric Stochastic Volatility Model

Mathematical Methods in the Applied Sciences, Volume 48, Issue 17, Page 16110-16121, 30 November 2025.
ABSTRACT The paper proposes a variational analysis of the 1‐hypergeometric stochastic volatility model for pricing European options. The methodology involves the derivation of estimates of the weak solution in a weighted Sobolev space. The weight is closely related to the stochastic volatility dynamic of the model.
José Da Fonseca, Wenjun Zhang
wiley   +1 more source

Random Attractor of Reaction‐Diffusion Hopfield Neural Networks Driven by Wiener Processes

Mathematical Problems in Engineering, Volume 2018, Issue 1, 2018., 2018
This paper studies the global existence and uniqueness of the mild solution for reaction‐diffusion Hopfield neural networks (RDHNNs) driven by Wiener processes by applying a Schauder fixed point theorem and a priori estimate; then the random attractor for this system is also studied by constructing proper random dynamical system.
Xiao Liang, Linshan Wang, Ruili Wang, Fazal M. Mahomed   +3 more
wiley   +1 more source

Invariance of Gaussian RKHSs Under Koopman Operators of Stochastic Differential Equations With Constant Matrix Coefficients

Proceedings in Applied Mathematics and Mechanics, Volume 25, Issue 1, March 2025.
ABSTRACT We consider the Koopman operator semigroup (Kt)t≥0$(K^t)_{t\ge 0}$ associated with stochastic differential equations of the form dXt=AXtdt+BdWt$dX_t = AX_t\,dt + B\,dW_t$ with constant matrices A$A$ and B$B$ and Brownian motion Wt$W_t$. We prove that the reproducing kernel Hilbert space HC$\mathbb {H}_C$ generated by a Gaussian kernel with a ...
Friedrich M. Philipp, Manuel Schaller, Karl Worthmann, Sebastian Peitz, Feliks Nüske   +4 more
wiley   +1 more source