Author:
De Bruyne Benjamin,Majumdar Satya N,Orland Henri,Schehr Grégory
Abstract
Abstract
We propose a method to exactly generate Brownian paths x
c
(t) that are constrained to return to the origin at some future time t
f
, with a given fixed area
A
f
=
∫
0
t
f
d
t
x
c
(
t
)
under their trajectory. We derive an exact effective Langevin equation with an effective force that accounts for the constraint. In addition, we develop the corresponding approach for discrete-time random walks, with arbitrary jump distributions including Lévy flights, for which we obtain an effective jump distribution that encodes the constraint. Finally, we generalise our method to other types of dynamical constraints such as a fixed occupation time on the positive axis
T
f
=
∫
0
t
f
d
t
Θ
x
c
(
t
)
or a fixed generalised quadratic area
A
f
=
∫
0
t
f
d
t
x
c
2
(
t
)
.
Subject
Statistics, Probability and Uncertainty,Statistics and Probability,Statistical and Nonlinear Physics
Cited by
10 articles.
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