On the Random Walk and Brownian Motion

DOI10.2307/1993657zbMath0279.60057OpenAlexW4252931703MaRDI QIDQ4765828

Frank B. Knight

Publication date: 1962

Full work available at URL: https://doi.org/10.2307/1993657

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Strong limit theorems (60F15) Brownian motion (60J65)

Related Items (17)

Strong approximation of fractional Brownian motion by moving averages of simple random walks. ⋮ Approximation of transport process by transport chain ⋮ Randomizing quantum walk ⋮ Finite approximation schemes for Lévy processes, and their application to optimal stopping problems ⋮ Periodicity of Grover walks on complete graphs with self-loops ⋮ Self-intersection local time of planar Brownian motion based on a strong approximation by random walks ⋮ A stochastically quasi-optimal search algorithm for the maximum of the simple random walk ⋮ One-dimensional quantum walks with a position-dependent coin ⋮ From Discrete to Continuous Financial Models: New Convergence Results For Option Pricing ⋮ An exponential functional of random walks ⋮ The average density of the path of planar Brownian motion ⋮ Stochastic integration based on simple, symmetric random walks ⋮ Sojourn Times and the Exact Hausdorff Measure of the Sample Path for Planar Brownian Motion ⋮ Random Walks and A Sojourn Density Process of Brownian Motion ⋮ On dynamic investment strategies ⋮ Diffusions as a limit of stretched Brownian motions ⋮ On strong invariance for local time of partial sums

Cites Work

• On the intrinsic form for second order differential operators
• A property of Brownian motion paths
• Some Theorems Concerning Brownian Motion
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