Quasi-Banach spaces of random variables and stochastic processes
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917363659571200 |
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| author | Kozachenko, Yuriy Mlavets, Yuriy Mokliachuk, Oleksandr |
| author_facet | Kozachenko, Yuriy Mlavets, Yuriy Mokliachuk, Oleksandr |
| contents | This book develops the theory of quasi-Banach $K_σ$-spaces $\mathbf{F}_ψ(Ω)$, $\mathbf{F}_ψ^*(Ω)$, and $D_{V,W}(Ω)$ of random variables and stochastic processes, extending the classical framework of Orlicz spaces, $Sub_φ(Ω)$ and $V(φ,ψ)$ spaces. The book consists of eleven chapters. The first two chapters establish the foundational theory: stochastic processes from quasi-Banach $K_σ$-spaces are introduced, and the fundamental properties of $\mathbf{F}_ψ(Ω)$ are studied in detail. The third chapter derives distribution estimates for suprema of processes from $\mathbf{F}_ψ^*(Ω)$, and the fourth addresses approximation theory in $SF_ψ(Ω)$. The fifth chapter examines Orlicz spaces and their connections to $\mathbf{F}_ψ(Ω)$. Chapters six and seven treat the pre-Banach $K_σ$-spaces $D_{V,W}(Ω)$, establishing their essential properties and evaluating reliability and accuracy of stochastic process models. The eighth chapter provides norm distribution estimates in $L_p(T)$ for processes from $\mathbf{F}_ψ(Ω)$. The ninth chapter develops the Monte Carlo method for multiple integrals over $\mathbb{R}^n$ with prescribed reliability and accuracy. The final two chapters treat modeling of $Sub_φ(Ω)$ processes - subclasses of $K_σ$-spaces - with given reliability and accuracy in $L_p(T)$ and $C(T)$ respectively. The results are substantially based on the authors' original work and that of their co-authors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_26002 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quasi-Banach spaces of random variables and stochastic processes Kozachenko, Yuriy Mlavets, Yuriy Mokliachuk, Oleksandr Statistics Theory Probability Primary: 60-02, Secondary: 60G07, 60G14, 60G15, 62M15, 65C05, 46E30 This book develops the theory of quasi-Banach $K_σ$-spaces $\mathbf{F}_ψ(Ω)$, $\mathbf{F}_ψ^*(Ω)$, and $D_{V,W}(Ω)$ of random variables and stochastic processes, extending the classical framework of Orlicz spaces, $Sub_φ(Ω)$ and $V(φ,ψ)$ spaces. The book consists of eleven chapters. The first two chapters establish the foundational theory: stochastic processes from quasi-Banach $K_σ$-spaces are introduced, and the fundamental properties of $\mathbf{F}_ψ(Ω)$ are studied in detail. The third chapter derives distribution estimates for suprema of processes from $\mathbf{F}_ψ^*(Ω)$, and the fourth addresses approximation theory in $SF_ψ(Ω)$. The fifth chapter examines Orlicz spaces and their connections to $\mathbf{F}_ψ(Ω)$. Chapters six and seven treat the pre-Banach $K_σ$-spaces $D_{V,W}(Ω)$, establishing their essential properties and evaluating reliability and accuracy of stochastic process models. The eighth chapter provides norm distribution estimates in $L_p(T)$ for processes from $\mathbf{F}_ψ(Ω)$. The ninth chapter develops the Monte Carlo method for multiple integrals over $\mathbb{R}^n$ with prescribed reliability and accuracy. The final two chapters treat modeling of $Sub_φ(Ω)$ processes - subclasses of $K_σ$-spaces - with given reliability and accuracy in $L_p(T)$ and $C(T)$ respectively. The results are substantially based on the authors' original work and that of their co-authors. |
| title | Quasi-Banach spaces of random variables and stochastic processes |
| topic | Statistics Theory Probability Primary: 60-02, Secondary: 60G07, 60G14, 60G15, 62M15, 65C05, 46E30 |
| url | https://arxiv.org/abs/2603.26002 |