Comment on “Spherical particle Brownian motion in viscous medium as non-Markovian random process” [Phys. Lett. A 375 (2011) 4113]

2013 ◽  
Vol 377 (34-36) ◽  
pp. 2251-2252
Author(s):  
Vladimir Lisy ◽  
Jana Tothova
Keyword(s):  
Brownian Motion ◽  
Random Process ◽  
Spherical Particle ◽  
Viscous Medium ◽  
Markovian Random Process

scholarly journals On the maximum drawdown of a Brownian motion

2004 ◽  
Vol 41 (1) ◽  
pp. 147-161 ◽  
Author(s):  
Malik Magdon-Ismail ◽  
Amir F. Atiya ◽  
Amrit Pratap ◽  
Yaser S. Abu-Mostafa
Keyword(s):  
Brownian Motion ◽  
Random Process ◽  
Infinite Series ◽  
Series Representation ◽  
Expected Value ◽  
Square Root ◽  
Brownian Motion With Drift ◽  
Negative Drift ◽  
Analytic Expression ◽  
Maximum Drawdown

The maximum drawdown at time T of a random process on [0,T] can be defined informally as the largest drop from a peak to a trough. In this paper, we investigate the behaviour of this statistic for a Brownian motion with drift. In particular, we give an infinite series representation of its distribution and consider its expected value. When the drift is zero, we give an analytic expression for the expected value, and for nonzero drift, we give an infinite series representation. For all cases, we compute the limiting (T → ∞) behaviour, which can be logarithmic (for positive drift), square root (for zero drift) or linear (for negative drift).

scholarly journals On the maximum drawdown of a Brownian motion

2004 ◽  
Vol 41 (01) ◽  
pp. 147-161 ◽  
Author(s):  
Malik Magdon-Ismail ◽  
Amir F. Atiya ◽  
Amrit Pratap ◽  
Yaser S. Abu-Mostafa
Keyword(s):  
Brownian Motion ◽  
Random Process ◽  
Infinite Series ◽  
Series Representation ◽  
Expected Value ◽  
Square Root ◽  
Brownian Motion With Drift ◽  
Negative Drift ◽  
Analytic Expression ◽  
Maximum Drawdown

The maximum drawdown at time T of a random process on [0,T] can be defined informally as the largest drop from a peak to a trough. In this paper, we investigate the behaviour of this statistic for a Brownian motion with drift. In particular, we give an infinite series representation of its distribution and consider its expected value. When the drift is zero, we give an analytic expression for the expected value, and for nonzero drift, we give an infinite series representation. For all cases, we compute the limiting (T → ∞) behaviour, which can be logarithmic (for positive drift), square root (for zero drift) or linear (for negative drift).

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