On the monotonicity of a function related to the local time of a symmetric Lévy process

2006 ◽  
Vol 76 (14) ◽  
pp. 1522-1528
Author(s):  
Renming Song ◽  
Zoran Vondraček
Keyword(s):  
Local Time ◽  
Lévy Process ◽  
Levy Process ◽  
Symmetric Lévy Process

Self-intersection local time of Additive levy process

2002 ◽  
Vol 22 (2) ◽  
pp. 261-268 ◽  
Author(s):  
Yuquan Zhong ◽  
Dike Hu
Keyword(s):  
Local Time ◽  
Lévy Process ◽  
Levy Process ◽  
Intersection Local Time

Local time of additive Levy process

2000 ◽  
Vol 5 (1) ◽  
pp. 007-012
Author(s):  
Zhong Yu-quan ◽  
Hu Di-he
Keyword(s):  
Local Time ◽  
Lévy Process ◽  
Levy Process

scholarly journals A geometric interpretation of the transition density of a symmetric Lévy process

2012 ◽  
Vol 55 (6) ◽  
pp. 1099-1126 ◽  
Author(s):  
Niels Jacob ◽  
Victorya Knopova ◽  
Sandra Landwehr ◽  
René L. Schilling
Keyword(s):  
Lévy Process ◽  
Transition Density ◽  
Geometric Interpretation ◽  
Levy Process ◽  
Symmetric Lévy Process

scholarly journals Analysis of stochastic fluid queues driven by local-time processes

2008 ◽  
Vol 40 (04) ◽  
pp. 1072-1103 ◽  
Author(s):  
Takis Konstantopoulos ◽  
Andreas E. Kyprianou ◽  
Paavo Salminen ◽  
Marina Sirviö
Keyword(s):  
Local Time ◽  
Lévy Process ◽  
Point Processes ◽  
Levy Process ◽  
Fluid Queue ◽  
Idle Period ◽  
Priority Service ◽  
Stationary Version ◽  
Palm Calculus ◽  
Stochastic Fluid

We consider a stochastic fluid queue served by a constant rate server and driven by a process which is the local time of a reflected Lévy process. Such a stochastic system can be used as a model in a priority service system, especially when the time scales involved are fast. The input (local time) in our model is typically (but not necessarily) singular with respect to the Lebesgue measure, a situation which, in view of the nonsmooth or bursty nature of several types of Internet traffic, is nowadays quite realistic. We first discuss how to rigorously construct the (necessarily) unique stationary version of the system under some natural stability conditions. We then consider the distribution of performance steady-state characteristics, namely, the buffer content, the idle period, and the busy period. These derivations are much based on the fact that the inverse of the local time of a Markov process is a Lévy process (a subordinator), hence making the theory of Lévy processes applicable. Another important ingredient in our approach is the use of Palm calculus for stationary random point processes and measures.

Linear MMSE Estimation of Large-Magnitude Symmetric Levy-Process Phase-Noise

2010 ◽  
Vol 58 (12) ◽  
pp. 3369-3374 ◽  
Author(s):  
Yeong-Tzay Su ◽  
Kainam Thomas Wong ◽  
Keang-Po Ho
Keyword(s):  
Phase Noise ◽  
Lévy Process ◽  
Levy Process ◽  
Large Magnitude ◽  
Mmse Estimation ◽  
Symmetric Lévy Process

scholarly journals Analysis of stochastic fluid queues driven by local-time processes

2008 ◽  
Vol 40 (4) ◽  
pp. 1072-1103 ◽  
Author(s):  
Takis Konstantopoulos ◽  
Andreas E. Kyprianou ◽  
Paavo Salminen ◽  
Marina Sirviö
Keyword(s):  
Local Time ◽  
Lévy Process ◽  
Point Processes ◽  
Levy Process ◽  
Fluid Queue ◽  
Idle Period ◽  
Priority Service ◽  
Stationary Version ◽  
Palm Calculus ◽  
Stochastic Fluid

We consider a stochastic fluid queue served by a constant rate server and driven by a process which is the local time of a reflected Lévy process. Such a stochastic system can be used as a model in a priority service system, especially when the time scales involved are fast. The input (local time) in our model is typically (but not necessarily) singular with respect to the Lebesgue measure, a situation which, in view of the nonsmooth or bursty nature of several types of Internet traffic, is nowadays quite realistic. We first discuss how to rigorously construct the (necessarily) unique stationary version of the system under some natural stability conditions. We then consider the distribution of performance steady-state characteristics, namely, the buffer content, the idle period, and the busy period. These derivations are much based on the fact that the inverse of the local time of a Markov process is a Lévy process (a subordinator), hence making the theory of Lévy processes applicable. Another important ingredient in our approach is the use of Palm calculus for stationary random point processes and measures.

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