An asymptotic formula for the Kolmogorov diffusion and a refinement of Sinai's estimates for the integral of Brownian motion

DOI10.3792/pjaa.70.271zbMath0820.60066OpenAlexW2069626006MaRDI QIDQ1805023

Yasuki Isozaki, Shinzo Watanabe

Publication date: 11 September 1995

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pjaa.70.271

zbMATH Keywords

Brownian motiontwo-dimensional diffusion processintegral of Brownian motion

Mathematics Subject Classification ID

Brownian motion (60J65) Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) (60J70)

Related Items (14)

Persistence probabilities of mixed FBM and other mixed processes ⋮ Asymptotics of the Persistence Exponent of Integrated Fractional Brownian Motion and Fractionally Integrated Brownian Motion ⋮ Survival exponents for some Gaussian processes ⋮ Universality of the asymptotics of the one-sided exit problem for integrated processes ⋮ Random walk with barycentric self-interaction ⋮ Positivity of integrated random walks ⋮ Clustering in a stochastic model of one-dimensional gas ⋮ Hitting law asymptotics for a fluctuating Brownian functional ⋮ The Vlasov-Poisson-Fokker-Planck equation in an interval with kinetic absorbing boundary conditions ⋮ Hitting of a line or a half-line in the plane by two-dimensional symmetric stable Lévy processes ⋮ On the probability that integrated random walks stay positive ⋮ Persistence Probabilities and Exponents ⋮ Integrated Brownian motion, conditioned to be positive ⋮ Local asymptotics for the area of random walk excursions

Cites Work

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• The inviscid Burgers equation with initial data of Brownian type
• Distribution of some functionals of the integral of a random walk
• Zufällige Bewegungen. (Zur Theorie der Brownschen Bewegung.)
• A winding problem for a resonator driven by a white noise
• On the first hitting place of the integrated Wiener process
• First-Passage Densities of a Two-Dimensional Process
• On the First Passage of the Integrated Wiener Process

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