Brownian Bridge

2008 ◽  
Keyword(s):  
Brownian Bridge

scholarly journals On the local time density of the reflecting Brownian bridge

2000 ◽  
Vol 13 (2) ◽  
pp. 125-136 ◽  
Author(s):  
Bernhard Gittenberger ◽  
Guy Louchard
Keyword(s):  
Limit Theorem ◽  
Local Time ◽  
Brownian Bridge ◽  
Direct Method ◽  
Random Mappings ◽  
A Direct Method ◽  
Time Density

Expressions for the multi-dimensional densities of Brownian bridge local time are derived by two different methods: A direct method based on Kac's formula for Brownian functionals and an indirect one based on a limit theorem for strata of random mappings.

Approximate exit probabilities for a Brownian bridge on a short time interval, and applications

1989 ◽  
Vol 21 (1) ◽  
pp. 1-19 ◽  
Author(s):  
H. R. Lerche ◽  
D. Siegmund
Keyword(s):  
Virial Coefficient ◽  
Large Deviation ◽  
Brownian Bridge ◽  
Exit Time ◽  
Second Virial Coefficient ◽  
Dimensional Euclidean Space ◽  
Time Interval ◽  
Short Time Interval ◽  
First Exit Time ◽  
Short Time

Let T be the first exit time of Brownian motion W(t) from a region ℛ in d-dimensional Euclidean space having a smooth boundary. Given points ξ0 and ξ1 in ℛ, ordinary and large-deviation approximations are given for Pr{T < ε |W(0) = ξ0, W(ε) = ξ 1} as ε → 0. Applications are given to hearing the shape of a drum and approximating the second virial coefficient.

scholarly journals Arboreal aperitifs: Space use and activity of a major songbird nest predator in a tropical Thailand forest

2021 ◽  
Author(s):  
Anji D’souza ◽  
George Gale ◽  
Benjamin Michael Marshall ◽  
Daphawan Khamcha ◽  
Surachit Waengsothorn ◽  
...  
Keyword(s):  
Brownian Bridge ◽  
Radio Telemetry ◽  
Space Use ◽  
Evergreen Forest ◽  
Boiga Irregularis ◽  
Forest Fragment ◽  
Predator Species ◽  
Avian Nest ◽  
Nest Predator ◽  
Nesting Season

ABSTRACTPredator-prey interactions are fundamental drivers of population dynamics, yet rarely are both predator and prey species simultaneously studied. Despite being significant, widespread avian nest predators, research on the ecology of Southeast Asian snakes in relation to birds remains scarce. The green cat snake (Boiga cyanea) is a primary nest predator, responsible for ≈24% of forest songbird depredation in Northeast Thailand. We explored both diurnal and nocturnal movements of 14 (5 male, 9 female) adult B. cyanea with radio-telemetry for an average of 68 ± 16 days per individual, between 21 October 2017 and 8 June 2019 in the dry evergreen forest of the Sakaerat Biosphere Reserve (SBR). We quantified area of space use (ha) and activity through motion variance (Ϭm2) during the study period using dynamic Brownian bridge movement models, and linked our findings to a simultaneously-run avian nest monitoring study, initiated in 2013 within the same forest fragment. On average, movements, space use and activity differed between males and females, and between the avian nesting and non-nesting seasons. Males moved 51.37 m/day farther than females. They used areas 15.09 ha larger than females, and their activity was 3.91 Ϭm2 higher than that of females. In general, individuals moved 50.30 m/day farther during the nesting season than the non-nesting season. The snakes used areas 9.84 ha larger during the nesting season than the non-nesting season, and their activity during the nesting season was 3.24 Ϭm2 higher than that during the non-nesting season. All individuals were exclusively nocturnal, moving throughout the night, and often descending from higher diurnal refugia (>2 m) to forage closer to the ground after sunset. Boiga cyanea activity followed a similar trend to that of the recorded nest depredations at SBR. Our study links snake activity to nest depredations in SBR. Our openly-available data may yield further insight when combined with other major avian nest predator species like the congeneric invasive brown tree snake (Boiga irregularis) on the island of Guam.

scholarly journals CONTINUITY PROPERTIES OF SCHRÖDINGER SEMIGROUPS WITH MAGNETIC FIELDS

2000 ◽  
Vol 12 (02) ◽  
pp. 181-225 ◽  
Author(s):  
KURT BRODERIX ◽  
DIRK HUNDERTMARK ◽  
HAJO LESCHKE
Keyword(s):  
Brownian Bridge ◽  
Integral Kernel ◽  
Dirichlet Boundary Conditions ◽  
Dimensional Euclidean Space ◽  
Kato Class ◽  
Vector Potentials ◽  
Continuity Properties ◽  
Scalar Potentials ◽  
General Configuration ◽  
Zero Vector

The objects of the present study are one-parameter semigroups generated by Schrödinger operators with fairly general electromagnetic potentials. More precisely, we allow scalar potentials from the Kato class and impose on the vector potentials only local Kato-like conditions. The configuration space is supposed to be an arbitrary open subset of multi-dimensional Euclidean space; in case that it is a proper subset, the Schrödinger operator is rendered symmetric by imposing Dirichlet boundary conditions. We discuss the continuity of the image functions of the semigroup and show local-norm-continuity of the semigroup in the potentials. Finally, we prove that the semigroup has a continuous integral kernel given by a Brownian-bridge expectation. Altogether, the article is meant to extend some of the results in B. Simon's landmark paper [Bull. Amer. Math. Soc.7 (1982) 447] to non-zero vector potentials and more general configuration spaces.

Brownian bridge asymptotics for random mappings

1992 ◽  
Vol 24 (4) ◽  
pp. 763-764
Author(s):  
D. J. Aldous
Keyword(s):  
Brownian Bridge ◽  
Random Mappings

The Brownian Bridge

2021 ◽  
pp. 235-242
Author(s):  
Rabi Bhattacharya ◽  
Edward C. Waymire
Keyword(s):  
Brownian Bridge

scholarly journals How linear reinforcement affects Donsker’s theorem for empirical processes

2020 ◽  
Vol 178 (3-4) ◽  
pp. 1173-1192 ◽  
Author(s):  
Jean Bertoin
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Long Range ◽  
Limit Theorems ◽  
Brownian Bridge ◽  
Empirical Processes ◽  
Constant Factor ◽  
Empirical Measure ◽  
Reinforced Random Walks ◽  
Bernoulli Processes

Abstract A reinforcement algorithm introduced by Simon (Biometrika 42(3/4):425–440, 1955) produces a sequence of uniform random variables with long range memory as follows. At each step, with a fixed probability $$p\in (0,1)$$ p ∈ ( 0 , 1 ) , $${\hat{U}}_{n+1}$$ U ^ n + 1 is sampled uniformly from $${\hat{U}}_1, \ldots , {\hat{U}}_n$$ U ^ 1 , … , U ^ n , and with complementary probability $$1-p$$ 1 - p , $${\hat{U}}_{n+1}$$ U ^ n + 1 is a new independent uniform variable. The Glivenko–Cantelli theorem remains valid for the reinforced empirical measure, but not the Donsker theorem. Specifically, we show that the sequence of empirical processes converges in law to a Brownian bridge only up to a constant factor when $$p<1/2$$ p < 1 / 2 , and that a further rescaling is needed when $$p>1/2$$ p > 1 / 2 and the limit is then a bridge with exchangeable increments and discontinuous paths. This is related to earlier limit theorems for correlated Bernoulli processes, the so-called elephant random walk, and more generally step reinforced random walks.

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