How small are the increments of a Wiener process?

DOI10.1016/0304-4149(78)90001-7zbMath0387.60032OpenAlexW2006876086MaRDI QIDQ1250477

Miklós Csörgő, Pál Révész

Publication date: 1978

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0304-4149(78)90001-7

Mathematics Subject Classification ID

Gaussian processes (60G15) Sums of independent random variables; random walks (60G50) Strong limit theorems (60F15) Brownian motion (60J65) Sample path properties (60G17)

Related Items (16)

The Csörgö-Révész modulus of non-differentiability of iterated Brownian motion ⋮ Law of the iterated logarithm for the increments of stable subordinators ⋮ Local functional limit theorems of increments for Brownian motion ⋮ A new class of strongly consistent variance estimators for steady-state simulations ⋮ How small are the increments of \(G\)-Brownian motion ⋮ Loi de type Chung en norme de Hölder pour les accroissements locaux du mouvement brownien. (Chung type law for increments of Brownian motion in Hölder norm) ⋮ Some convergence problems about the increments of a wiener process ⋮ The rate of convergence in the functional limit theorem for increments of a Brownian motion ⋮ Inner rates of coverage of Strassen type sets by increments of the uniform empirical and quantile processes ⋮ Asymptotic results for random processes ⋮ [https://portal.mardi4nfdi.de/wiki/Publication:3339856 On the functional form of L�vy's modulus of continuity for Brownian motion] ⋮ Strassen type limit points for moving averages of a wiener process ⋮ The multifractal nature of Volterra-Lévy processes ⋮ The moduli of non-differentiability for Gaussian random fields with stationary increments ⋮ Limit laws for local times of the Brownian sheet ⋮ The Csörgő-Révész moduli of non-differentiability of fractional Brownian motion

Cites Work

• The other law of the iterated logarithm
• On the oscillation of the Brownian motion process
• On a new law of large numbers
• Regularity of irregularities on a Brownian path
• Small Deviations in a Space of Trajectories
• How big are the increments of a multi-parameter Wiener process?
• A strong law for the maximum cumulative sum of independent random variables
• On the Maximum Partial Sums of Sequences of Independent Random Variables

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