Construction and sample path properties of Brownian house-moving between two curves
Kensuke Ishitani, Daisuke Hatakenaka, Keisuke Suzuki
TL;DR
This paper constructs a new stochastic process called Brownian house-moving, which is a Brownian bridge constrained between two curves, and analyzes its sample path properties.
Contribution
It introduces the construction of Brownian house-moving via weak convergence of conditioned Brownian processes and studies its path properties.
Findings
Successful construction of Brownian house-moving process
Analysis of sample path regularity and properties
Extension of conditioned Brownian motion theory
Abstract
This study aims to construct a stochastic process called "Brownian house-moving," which is a Brownian bridge conditioned to stay between two curves. To construct this process, statements are prepared on the weak convergence of conditioned Brownian motions, conditioned Brownian bridges, and conditioned three-dimensional Bessel bridges. Moreover, the sample path properties of Brownian house-moving are studied as well.
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Taxonomy
Topicsadvanced mathematical theories · Stochastic processes and financial applications · Diffusion and Search Dynamics