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## Filters

##
###
Construction of the paths of Brownian motions on star graphs I

2012
*
Communications on Stochastic Analysis
*

In

doi:10.31390/cosa.6.2.04
fatcat:fwrwwo7ojbg6bjdsd7lzxizg4q
*the*present article and its follow-up article [23] pathwise*constructions**of**Brownian**motions*which satisfy all possible boundary conditions at*the*vertex*of*star graphs are given. ... In*the*opinion*of**the*authors this leads to much simpler*computations**of**the*transition kernels than those in [17, 18, 20] for*a**Brownian**motion**on*ℝ + . ...*The**Brownian**motions**constructed*here*on*star graphs are then*the*basic building blocks*of**Brownian**motions**on*general, finite metric graphs in*the*article [24]*of**the*present authors. ...##
###
An Efficient Algorithm to Simulate a Brownian Motion Over Irregular Domains

2010
*
Communications in Computational Physics
*

This coupling algorithm has

doi:10.4208/cicp.240209.031209a
fatcat:mcy7gujib5c7jodm4knma3hety
*the*advantage to be able to*compute**the*exit time and*the*exit position*of**a**Brownian**motion*from an irregular bounded domain (with corners at*the*boundary), and being*of*order ... In this paper, we present an algorithm to simulate*a**Brownian**motion*by coupling two numerical schemes:*the*Euler scheme with*the*random walk*on**the*hyper-rectangles. ... So far,*the**Brownian**motion*is characterized by*the*solution*of*some PDE. Conversely,*the*solution*of**a*PDE can be*computed*using*the**Brownian**motion*. ...##
###
Stratified sampling and quasi-Monte Carlo simulation of Lévy processes

2006
*
Monte Carlo Methods and Applications
*

We provide

doi:10.1515/156939606778705155
fatcat:otpclcm2abfl3amsjifpenfvy4
*a*method for*the*generation*of*paths*of*Lévy processes which has many*of**the*benefits that*the**Brownian*bridge*construction*has for*Brownian**motion*. ... As*a*numerical example we consider*the*problem*of*pricing an asian option in*the*so-called hyperbolic market model. ...*on**a**Brownian**motion*. ...##
###
Construction of the paths of Brownian motions on star graphs II

2012
*
Communications on Stochastic Analysis
*

In this article and its predecessor [9] , pathwise

doi:10.31390/cosa.6.2.05
fatcat:5bcspnxzkjeyhet3t3hsfvqgdq
*constructions**of**Brownian**motions*which satisfy all possible boundary conditions at*the*vertex*of*star graphs are given. ... In article I we*constructed**the*Walsh process*on**the*single vertex graph from*a*standard*Brownian**motion**on**the*real line. ... Hence, altogether we have shown that is*a**Brownian**motion**on*in*the*sense*of*definition 1.1. Now we want to*compute**the*generator*of*, and first we argue that is not*a*trap for . ...##
###
Sticky Brownian motion as the strong limit of a sequence of random walks

1991
*
Stochastic Processes and their Applications
*

We provide here

doi:10.1016/0304-4149(91)90080-v
fatcat:6eucef3zufgytjlkq6s2urbfai
*a**constructive*definition*of**the*sticky*Brownian**motion*as we show that it is*the*almost sure uniform limit*of*path functions*of**a*time changed random walk. ...*The*transition distribution*of*this process is also derived. F" P,) P,-a.s. W*(t) has speed 0304.4149/91/$03.50 @ 1991-Elsevier Science Publishers B.V. (North-Holland) ... In most texts, it is referred to*the*sticky*Brownian**motion*,*a**Brownian**motion*'slowly' reflecting at zero or with*a*sticky boundary at zero. Here we*construct**a*sticky*Brownian**motion**on*(-00, +*a*). ...##
###
Page 1948 of Mathematical Reviews Vol. , Issue 99c
[page]

1991
*
Mathematical Reviews
*

*The*authors take

*Brownian*

*motion*

*on*

*the*Sierpinski gasket and

*construct*

*a*superprocess over this spatial

*motion*. ...

*The*proofs use

*the*scaling

*of*

*the*transition density

*of*

*the*

*Brownian*

*motion*

*on*

*the*gasket. ...

##
###
A multiscale guide to Brownian motion

2015
*
Journal of Physics A: Mathematical and Theoretical
*

We revise

doi:10.1088/1751-8113/49/4/043001
fatcat:zollpg3nebelhpcf2djhsawvxi
*the*Levy's*construction**of**Brownian**motion*as*a*simple though still rigorous approach to operate with various Gaussian processes. ... Such*a*wavelet representation gives*a*closed formula mapping*of**the*unit interval onto*the*functional space*of**Brownian*paths. ...*BROWNIAN**MOTION*In this section, we derive*a*wavelet representation*of**Brownian**motion*in*a*simple explicit way, allowing*one*to gain an intuitive feeling*of*this*constructive*approach.*A*. ...##
###
Page 3771 of Mathematical Reviews Vol. , Issue 98F
[page]

1998
*
Mathematical Reviews
*

*The*

*construction*relies

*on*

*a*clever coupling argument which

*constructs*

*a*sequence

*of*Moran models

*on*

*the*same sample space as

*the*“look down” particles such that

*the*first m components share

*the*same empirical ... Summary: “Let X(r) (¢ € R”) be

*a*fractional

*Brownian*

*motion*

*of*index

*a*in R¢. ...

##
###
Hedging with Monte Carlo Simulation
[chapter]

2002
*
Applied Optimization
*

Monte Carlo simulation provides

doi:10.1007/978-1-4757-3613-7_18
fatcat:52iwp5znfbesnozrw6mggnxoyi
*a*simple procedure to price securities numerically; however, it does not immediately yield*the*weights necessary to*construct**a*replicating portfolio. ... Compared to*the*alternative procedure,*the*method we suggest has*the*advantage that*the**computational*cost is independent*of**the*number*of*dimensions (unlike*the*traditional procedure where*the*cost increases ... In this Section we describe*the*implementation*of**the*RVM in*a*setting with more than*one**Brownian**motion*process. ...##
###
Effective Langevin equations for constrained stochastic processes
[article]

2015
*
arXiv
*
pre-print

*The*method is illustrated

*on*

*the*generation

*of*

*Brownian*bridges,

*Brownian*meanders,

*Brownian*excursions and constrained Ornstein-Uehlenbeck processes. ... In addition, we show how to solve this equation in

*the*case

*of*

*a*general force acting

*on*

*the*particle. As an example, we show how to generate constrained path joining

*the*two minima

*of*

*a*double-well. ... ACKNOWLEDGMENTS We thank

*the*hospitality

*of*

*the*Galileo Galilei Institute (Florence) during

*the*workshop "Advances in Nonequilibrium Statistical Mechanics: large deviations and long-range correlations, ...

##
###
Fractional Brownian fields, duality, and martingales
[chapter]

2006
*
High Dimensional Probability
*

*The*Gaussian field, due to inherited "duality", reveals

*a*new way

*of*

*constructing*martingales associated with

*the*odd and even part

*of*

*a*fractional

*Brownian*

*motion*and therefore

*of*

*the*fractional

*Brownian*... In this paper

*the*whole family

*of*fractional

*Brownian*

*motions*is

*constructed*as

*a*single Gaussian field indexed by time and

*the*Hurst index simultaneously. ... That property leads to

*a*

*construction*

*of*martingales associated to fractional

*Brownian*

*motions*. ...

##
###
Monte Carlo methods for fissured porous media: a gridless approach *

2004
*
Monte Carlo Methods and Applications
*

In this article, we present two Monte Carlo methods to solve some problems related to

doi:10.1515/mcma.2004.10.3-4.385
fatcat:3btb24kmgjekhfid72xrtb7wzm
*the*Darcy law in geophysics. Both methods do not require any discretization and are exact methods. ... Now, locally around*a*vertex,*a**Brownian**motion*(X, P x )*on**a*graph is*a*generalization*of**the*Skew*Brownian**motion*:*on*each edge,*the*process behaves like*a**one*-dimensional*Brownian**motion*until it hit ... For any α ∈ (0, 1), it is possible to*construct**a*stochastic process called*a*Skew*Brownian**motion*such that: X behaves like*a**Brownian**motion**on*R * + and R * − (that is*the*infinitesimal generator is ...##
###
Page 6907 of Mathematical Reviews Vol. , Issue 96k
[page]

1996
*
Mathematical Reviews
*

*The*key point to T. Lindstrem’s

*construction*

*of*

*Brownian*

*motion*

*on*nested fractals [Mem. Amer. Math. ...

*The*paper contains

*a*

*construction*

*of*

*a*pair

*of*planar

*Brownian*

*motions*starting from

*the*origin and conditioned not to intersect until they hit

*the*unit circle. ...

##
###
On White Noise Space and Levy's Brownian Motion on the Circle
[article]

2020
*
arXiv
*
pre-print

In this article, we show that

arXiv:1911.03374v2
fatcat:navb5rai4fa35hyj6t4nuskfiy
*the**Brownian**motion**on**the*circle*constructed*in Levy (1959) is*a*regular Euclidean*Brownian**motion**on**the*half-circle with its own mirror image*on**the*other half-circle, ... This raises*the*question*of*what*the*white noise is*on**the*circle. We then formally define*the*white noise space and its associated*Brownian*bridge. ... In Euclidean spaces,*a*white noise, sometimes, can be thought*of*as*the*generalized derivative*of**a**Brownian**motion*. ...##
###
Page 5191 of Mathematical Reviews Vol. , Issue 86k
[page]

1986
*
Mathematical Reviews
*

To avoid

*a*certain dependency*on*dimension which appears in Pinsky’s con- struction,*the*author uses*the*central hitting measure*of**the*surface*of**the*unit ball with respect to*the**Brownian**motion**on**the*... In this expository article*the*author recapitulates his construc- tion*of**Brownian**motion**on**a*smooth manifold as*a*weak limit*of*“Isotropic transport processes”. ...
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