Existence of continuous and càdlàg versions for cylindrical processes in the dual of a nuclear space
CA Fonseca-Mora - Journal of Theoretical Probability, 2018 - Springer
Let Φ Φ be a nuclear space and let Φ'_ β Φ β′ denote its strong dual. In this paper, we
introduce sufficient conditions for a cylindrical process in Φ'Φ′ to have a version that is a …
introduce sufficient conditions for a cylindrical process in Φ'Φ′ to have a version that is a …
Stochastic integration and stochastic PDEs driven by jumps on the dual of a nuclear space
CA Fonseca-Mora - … and Partial Differential Equations: Analysis and …, 2018 - Springer
We develop a novel theory of weak and strong stochastic integration for cylindrical
martingale-valued measures taking values in the dual of a nuclear space. This is applied to …
martingale-valued measures taking values in the dual of a nuclear space. This is applied to …
Lévy processes and infinitely divisible measures in the dual of a nuclear space
CA Fonseca-Mora - Journal of Theoretical Probability, 2020 - Springer
Let Φ Φ be a nuclear space and let Φ'_ β Φ β′ denote its strong dual. In this work, we prove
the existence of càdlàg versions, the Lévy–Itô decomposition and the Lévy–Khintchine …
the existence of càdlàg versions, the Lévy–Itô decomposition and the Lévy–Khintchine …
Convolution type stochastic Volterra equations
A Karczewska - arXiv preprint arXiv:0712.4357, 2007 - arxiv.org
The aim of this work is to present, in self-contained form, results concerning fundamental
and the most important questions related to linear stochastic Volterra equations of …
and the most important questions related to linear stochastic Volterra equations of …
Regularity of solutions to stochastic Volterra equations
A Karczewska, J Zabczyk - … Nazionale dei Lincei. Classe di Scienze …, 2000 - dml.mathdoc.fr
We study regularity of stochastic convolutions solving Volterra equations on R d driven by a
spatially homogeneous Wiener process. General results are applied to stochastic parabolic …
spatially homogeneous Wiener process. General results are applied to stochastic parabolic …
Gaussian and Non–Gaussian Distribution–Valued Ornstein–Uhlenbeck Processes
T Bojdecki, LG Gorostiza - Canadian journal of mathematics, 1991 - cambridge.org
Generalized (distribution-valued) Ornstein-Uhlenbeck processes, which by definition are
solutions of generalized Langevin equations, arise in many investigations on fluctuation …
solutions of generalized Langevin equations, arise in many investigations on fluctuation …
Self-intersection local time for Gaussian G′(Rd)-processes: Existence, path continuity and examples
T Bojdecki, LG Gorostiza - Stochastic processes and their applications, 1995 - Elsevier
In this paper we develop a criterion for existence or non-existence of self-intersection local
time (SILT) for a wide class of Gaussian L′(R d)-valued processes, we show that quite …
time (SILT) for a wide class of Gaussian L′(R d)-valued processes, we show that quite …
SELF-INTERSECTION LOCAL TIME FOR -WIENER PROCESSES AND RELATED ORNSTEIN–UHLENBECK PROCESSES
T Bojdecki, LG Gorostiza - Infinite Dimensional Analysis, Quantum …, 1999 - World Scientific
Existence and continuity results are obtained for self-intersection local time of-valued
Ornstein–Uhlenbeck processes, where X0 is Gaussian, Wt is an-Wiener process …
Ornstein–Uhlenbeck processes, where X0 is Gaussian, Wt is an-Wiener process …
Stochastic integration in Hilbert spaces with respect to cylindrical martingale-valued measures
AE Alvarado-Solano, CA Fonseca-Mora - arXiv preprint arXiv:2001.09080, 2020 - arxiv.org
In this work we introduce a theory of stochastic integration for operator-valued integrands
with respect to some classes of cylindrical martingale-valued measures in Hilbert spaces …
with respect to some classes of cylindrical martingale-valued measures in Hilbert spaces …
Asymptotic fluctuations and critical dimension for a two-level branching system
LG Gorostiza - Bernoulli, 1996 - projecteuclid.org
The high-density asymptotic behaviour of a two-level branching system in Rd is studied. In
the finite-variance case, a fluctuation limit process is obtained which is characterized as a …
the finite-variance case, a fluctuation limit process is obtained which is characterized as a …