On a conditioned Brownian motion and a maximum principle on the disk

2004 ◽  
Vol 93 (1) ◽  
pp. 309-329 ◽  
Author(s):  
A. Dall'Acqua ◽  
H. -C. Grunau ◽  
G. H. Sweers
Keyword(s):  
Brownian Motion ◽  
Maximum Principle ◽  
Conditioned Brownian Motion

Malliavin calculus used to derive a stochastic maximum principle for system driven by fractional Brownian and standard Wiener motions with application

2020 ◽  
Vol 28 (4) ◽  
pp. 291-306
Author(s):  
Tayeb Bouaziz ◽  
Adel Chala
Keyword(s):  
Brownian Motion ◽  
Maximum Principle ◽  
Control Problem ◽  
Fractional Brownian Motion ◽  
Stochastic Control ◽  
Malliavin Calculus ◽  
Stochastic Maximum Principle ◽  
Hurst Parameter ◽  
Principle Of Optimality ◽  
Initial Cost

AbstractWe consider a stochastic control problem in the case where the set of the control domain is convex, and the system is governed by fractional Brownian motion with Hurst parameter {H\in(\frac{1}{2},1)} and standard Wiener motion. The criterion to be minimized is in the general form, with initial cost. We derive a stochastic maximum principle of optimality by using two famous approaches. The first one is the Doss–Sussmann transformation and the second one is the Malliavin derivative.

The lifetime of conditioned Brownian motion in planar domains of infinite area

1991 ◽  
Vol 87 (4) ◽  
pp. 469-487 ◽  
Author(s):  
Jianming Xu
Keyword(s):  
Brownian Motion ◽  
Planar Domains ◽  
Conditioned Brownian Motion

The lifetime of conditioned Brownian motion

1983 ◽  
Vol 65 (1) ◽  
pp. 1-11 ◽  
Author(s):  
M. Cranston ◽  
T. R. McConnell
Keyword(s):  
Brownian Motion ◽  
Conditioned Brownian Motion

scholarly journals On the lifetime of a conditioned Brownian motion in the ball

2007 ◽  
Vol 335 (1) ◽  
pp. 389-405 ◽  
Author(s):  
Anna Dall'Acqua
Keyword(s):  
Brownian Motion ◽  
Conditioned Brownian Motion

scholarly journals A stochastic maximum principle for processes driven by fractional Brownian motion

2002 ◽  
Vol 100 (1-2) ◽  
pp. 233-253 ◽  
Author(s):  
Francesca Biagini ◽  
Yaozhong Hu ◽  
Bernt Øksendal ◽  
Agnès Sulem
Keyword(s):  
Brownian Motion ◽  
Maximum Principle ◽  
Fractional Brownian Motion ◽  
Stochastic Maximum Principle

scholarly journals Heat kernel, eigenfunctions, and conditioned Brownian motion in planar domains

1989 ◽  
Vol 84 (1) ◽  
pp. 188-200 ◽  
Author(s):  
Rodrigo Bañuelos ◽  
Burgess Davis
Keyword(s):  
Brownian Motion ◽  
Heat Kernel ◽  
Planar Domains ◽  
Conditioned Brownian Motion

The lifetime of conditioned Brownian motion in certain Lipschitz domains

1987 ◽  
Vol 75 (1) ◽  
pp. 55-65 ◽  
Author(s):  
R. Dante DeBlassie
Keyword(s):  
Brownian Motion ◽  
Lipschitz Domains ◽  
Conditioned Brownian Motion

scholarly journals Extremal problems for conditioned brownian motion and the hyperbolic metric

2000 ◽  
Vol 50 (5) ◽  
pp. 1507-1532 ◽  
Author(s):  
Rodrigo Bañuelos ◽  
Tom Carroll
Keyword(s):  
Brownian Motion ◽  
Extremal Problems ◽  
Hyperbolic Metric ◽  
The Hyperbolic Metric ◽  
Conditioned Brownian Motion

scholarly journals Conditioned Brownian motion and hyperbolic geodesics in simply connected domains.

1993 ◽  
Vol 40 (2) ◽  
pp. 321-332 ◽  
Author(s):  
Rodrigo Bañuelos ◽  
Tom Carroll
Keyword(s):  
Brownian Motion ◽  
Conditioned Brownian Motion ◽  
Simply Connected ◽  
Simply Connected Domains ◽  
Hyperbolic Geodesics
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