scholarly journals First-passage-time exponent for higher-order random walks:  Using Lévy flights

2001 ◽  
Vol 64 (1) ◽  
Author(s):  
J. M. Schwarz ◽  
Ron Maimon
Keyword(s):  
Random Walks ◽  
First Passage Time ◽  
Passage Time ◽  
Higher Order ◽  
First Passage ◽  
Lévy Flights ◽  
Levy Flights ◽  
Time Exponent

scholarly journals First passage time moments of asymmetric Lévy flights

2020 ◽  
Vol 53 (27) ◽  
pp. 275002 ◽  
Author(s):  
Amin Padash ◽  
Aleksei V Chechkin ◽  
Bartłomiej Dybiec ◽  
Marcin Magdziarz ◽  
Babak Shokri ◽  
...  
Keyword(s):  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
Lévy Flights ◽  
Levy Flights

scholarly journals Leapover Lengths and First Passage Time Statistics for Lévy Flights

2007 ◽  
Vol 99 (16) ◽  
Author(s):  
Tal Koren ◽  
Michael A. Lomholt ◽  
Aleksei V. Chechkin ◽  
Joseph Klafter ◽  
Ralf Metzler
Keyword(s):  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
Lévy Flights ◽  
Levy Flights

scholarly journals Skewness and Kurtosis in Stochastic Thermodynamics

2021 ◽  
Author(s):  
Andre Cardoso Barato ◽  
Taylor Wampler
Keyword(s):  
Entropy Production ◽  
Average Rate ◽  
First Passage Time ◽  
Passage Time ◽  
Higher Order ◽  
Upper And Lower Bounds ◽  
Thermodynamic Force ◽  
First Passage ◽  
Stochastic Thermodynamics ◽  
Skewness And Kurtosis

Abstract The thermodynamic uncertainty relation is a prominent result in stochastic thermodynamics that provides a bound on the fluctuations of any thermodynamic flux, also known as current, in terms of the average rate of entropy production. Such fluctuations are quantified by the second moment of the probability distribution of the current. The role of higher order standardized moments such as skewness and kurtosis remains largely unexplored. We analyze the skewness and kurtosis associated with the first passage time of thermodynamic currents within the framework of stochastic thermodynamics. We develop a method to evaluate higher order standardized moments associated with the first passage time of any current. For systems with a unicyclic network of states, we conjecture upper and lower bounds on skewness and kurtosis associated with entropy production. These bounds depend on the number of states and the thermodynamic force that drives the system out of equilibrium. We show that these bounds for skewness and kurtosis do not hold for multicyclic networks. We discuss the application of our results to infer an underlying network of states.

Calculations of first passage time of delayed tree-like networks

2015 ◽  
Vol 29 (28) ◽  
pp. 1550200
Author(s):  
Shuai Wang ◽  
Weigang Sun ◽  
Song Zheng
Keyword(s):  
Random Walks ◽  
First Passage Time ◽  
Passage Time ◽  
The Novel ◽  
Mean First Passage Time ◽  
First Passage ◽  
Initial Node ◽  
Network Parameters ◽  
Self Similar ◽  
The Mean

In this paper, we study random walks in a family of delayed tree-like networks controlled by two network parameters, where an immobile trap is located at the initial node. The novel feature of this family of networks is that the existing nodes have a time delay to give birth to new nodes. By the self-similar network structure, we obtain exact solutions of three types of first passage time (FPT) measuring the efficiency of random walks, which includes the mean receiving time (MRT), mean sending time (MST) and mean first passage time (MFPT). The obtained results show that the MRT, MST and MFPT increase with the network parameters. We further show that the values of MRT, MST and MFPT are much shorter than the nondelayed counterpart, implying that the efficiency of random walks in delayed trees is much higher.

scholarly journals Mean first-passage time for random walks on the T-graph

2009 ◽  
Vol 11 (10) ◽  
pp. 103043 ◽  
Author(s):  
Zhongzhi Zhang ◽  
Yuan Lin ◽  
Shuigeng Zhou ◽  
Bin Wu ◽  
Jihong Guan
Keyword(s):  
Random Walks ◽  
First Passage Time ◽  
Passage Time ◽  
Mean First Passage Time ◽  
First Passage

A Recursion Formula for the Moments of the First Passage Time of the Ornstein-Uhlenbeck Process

2015 ◽  
Vol 52 (02) ◽  
pp. 595-601
Author(s):  
Dirk Veestraeten
Keyword(s):  
Lower Order ◽  
First Passage Time ◽  
Recursion Formula ◽  
Passage Time ◽  
Higher Order ◽  
First Passage ◽  
Uhlenbeck Process ◽  
Higher Order Moments ◽  
Ornstein Uhlenbeck Process

In this paper we use the Siegert formula to derive alternative expressions for the moments of the first passage time of the Ornstein-Uhlenbeck process through a constant threshold. The expression for the nth moment is recursively linked to the lower-order moments and consists of only n terms. These compact expressions can substantially facilitate (numerical) applications also for higher-order moments.

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