scholarly journals A Note on a Sample-Path Rate Conservation Law and its Relationship with H = λG

1991 ◽  
Vol 23 (03) ◽  
pp. 662-665
Author(s):  
Karl Sigman
Keyword(s):  
Conservation Law ◽  
Sample Path ◽  
The Other ◽  
Final Remark

We present a simple sample-path version of the rate conservation law (of Miyazawa) and then show that the H = λG law (of Heyman and Stidham) is essentially the same law, that is, either one can be derived from the other. As a final remark we illustrate the use of both laws jointly to quickly obtain a queueing result.

scholarly journals A Note on a Sample-Path Rate Conservation Law and its Relationship withH=λG

1991 ◽  
Vol 23 (3) ◽  
pp. 662-665 ◽  
Author(s):  
Karl Sigman
Keyword(s):  
Conservation Law ◽  
Sample Path ◽  
The Other ◽  
Final Remark

We present a simple sample-path version of the rate conservation law (of Miyazawa) and then show that theH=λGlaw (of Heyman and Stidham) is essentially the same law, that is, either one can be derived from the other. As a final remark we illustrate the use of both laws jointly to quickly obtain a queueing result.

Coupled systems of two-dimensional turbulence

2013 ◽  
Vol 732 ◽  
Author(s):  
Rick Salmon
Keyword(s):  
Hamiltonian System ◽  
Energy Conservation ◽  
Strong Correlation ◽  
Conservation Law ◽  
Hamiltonian Dynamics ◽  
Coupled Systems ◽  
The Other ◽  
Two Dimensional ◽  
Coherent Vortices ◽  
Fluid Particles

AbstractOrdinary two-dimensional turbulence corresponds to a Hamiltonian dynamics that conserves energy and the vorticity on fluid particles. This paper considers coupled systems of two-dimensional turbulence with three distinct governing dynamics. One is a Hamiltonian dynamics that conserves the vorticity on fluid particles and a quantity analogous to the energy that causes the system members to develop a strong correlation in velocity. The other two dynamics considered are non-Hamiltonian. One conserves the vorticity on particles but has no conservation law analogous to energy conservation; the other conserves energy and enstrophy but it does not conserve the vorticity on fluid particles. The coupled Hamiltonian system behaves like two-dimensional turbulence, even to the extent of forming isolated coherent vortices. The other two dynamics behave very differently, but the behaviours of all four dynamics are accurately predicted by the methods of equilibrium statistical mechanics.

NONLINEAR DIFFUSION EQUATION WITH A PERTURBED CONVECTIONTERM: POTENTIAL SYMMETRIES WITH RESPECT TO THE SECOND CONSERVATION LAW

2021 ◽  
Vol 10 (5) ◽  
pp. 2611-2624
Author(s):  
O.K. Narain ◽  
F.M. Mahomed
Keyword(s):  
Diffusion Equation ◽  
Conservation Law ◽  
Nonlinear Diffusion ◽  
Nonlinear Diffusion Equation ◽  
The Other ◽  
Linear Case ◽  
Exact Equation ◽  
Convection Term ◽  
Potential Symmetries ◽  
Perturbed Equation

We consider the nonlinear diffusion equation with a perturbed convection term. The potential symmetries for the exact equation with respect to the second conservation law are classified. It is found that these exist only in the linear case. It is further shown that no nontrivial approximate potential symmetries of order one exists for the perturbed equation with respect to the other conservation law.

scholarly journals On the Generation of Infinitely Many Conservation Laws of the Black-Scholes Equation

Computation ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 65
Author(s):  
Winter Sinkala
Keyword(s):  
Differential Equations ◽  
Conservation Laws ◽  
Conservation Law ◽  
The Other ◽  
Multiplier Method ◽  
Lie Point Symmetries ◽  
Mathematical Study ◽  
Black Scholes

Construction of conservation laws of differential equations is an essential part of the mathematical study of differential equations. In this paper we derive, using two approaches, general formulas for finding conservation laws of the Black-Scholes equation. In one approach, we exploit nonlinear self-adjointness and Lie point symmetries of the equation, while in the other approach we use the multiplier method. We present illustrative examples and also show how every solution of the Black-Scholes equation leads to a conservation law of the same equation.

scholarly journals The connections of pseudo-Finsler spaces

2014 ◽  
Vol 11 (07) ◽  
pp. 1460025 ◽  
Author(s):  
E. Minguzzi
Keyword(s):  
General Relativity ◽  
Conservation Law ◽  
Finsler Geometry ◽  
The Other ◽  
Finsler Spaces ◽  
Dynamical Equations ◽  
Nonlinear Connection ◽  
Cartan Torsion ◽  
The Mean ◽  
Mean Cartan Torsion

We give an introduction to (pseudo-)Finsler geometry and its connections. For most results we provide short and self-contained proofs. Our study of the Berwald nonlinear connection is framed into the theory of connections over general fibered spaces pioneered by Mangiarotti, Modugno and other scholars. The main identities for the linear Finsler connection are presented in the general case, and then specialized to some notable cases like Berwald's, Cartan's or Chern–Rund's. In this way it becomes easy to compare them and see the advantages of one connection over the other. Since we introduce two soldering forms we are able to characterize the notable Finsler connections in terms of their torsion properties. As an application, the curvature symmetries implied by the compatibility with a metric suggest that in Finslerian generalizations of general relativity the mean Cartan torsion vanishes. This observation allows us to obtain dynamical equations which imply a satisfactory conservation law. The work ends with a discussion of yet another Finsler connection which has some advantages over Cartan's and Chern–Rund's.

A note on stochastic decomposition in a GI/G/1 queue with vacations or set-up times

1985 ◽  
Vol 22 (02) ◽  
pp. 419-428 ◽  
Author(s):  
Bharat T. Doshi
Keyword(s):  
Steady State ◽  
Waiting Time ◽  
Sample Path ◽  
The Other ◽  
Independent Random Variables ◽  
Recurrence Time ◽  
Stochastic Decomposition ◽  
Set Up ◽  
Forward Recurrence Time ◽  
Main Model

In this note we prove some stochastic decomposition results for variations of theGI/G/1 queue. Our main model is aGI/G/1 queue in which the server, when it becomes idle, goes on a vacation for a random length of time. On return from vacation, if it finds customers waiting, then it starts serving the first customer in the queue. Otherwise it takes another vacation and so on. Under fairly general conditions the waiting time of an arbitrary customer, in steady state, is distributed as the sum of two independent random variables: one corresponding to the waiting time without vacations and the other to the stationary forward recurrence time of the vacation. This extends the decomposition result of Gelenbe and Iasnogorodski [5]. We use sample path arguments, which are also used to prove stochastic decomposition in aGI/G/1 queue with set-up time.

Comparing counting processes and queues

1981 ◽  
Vol 13 (1) ◽  
pp. 207-220 ◽  
Author(s):  
Ward Whitt
Keyword(s):  
Stochastic Processes ◽  
Probability Space ◽  
Sample Path ◽  
The Other ◽  
Time Dependent ◽  
Queueing Models ◽  
Counting Processes ◽  
Stochastic Comparisons ◽  
Partial Orderings ◽  
Queueing Processes

Several partial orderings of counting processes are introduced and applied to compare stochastic processes in queueing models. The conditions for the queueing comparisons involve the counting processes associated with the interarrival and service times. The two queueing processes being compared are constructed on the same probability space so that each sample path of one process lies below the corresponding sample path of the other process. Stochastic comparisons between the processes and monotone functionals of the processes follow immediately from this construction. The stochastic comparisons are useful to obtain bounds for intractable systems. For example, the approach here yields bounds for queues with time-dependent arrival rates.

Comparing counting processes and queues

1981 ◽  
Vol 13 (01) ◽  
pp. 207-220 ◽  
Author(s):  
Ward Whitt
Keyword(s):  
Stochastic Processes ◽  
Probability Space ◽  
Sample Path ◽  
The Other ◽  
Time Dependent ◽  
Queueing Models ◽  
Counting Processes ◽  
Stochastic Comparisons ◽  
Partial Orderings ◽  
Queueing Processes

Several partial orderings of counting processes are introduced and applied to compare stochastic processes in queueing models. The conditions for the queueing comparisons involve the counting processes associated with the interarrival and service times. The two queueing processes being compared are constructed on the same probability space so that each sample path of one process lies below the corresponding sample path of the other process. Stochastic comparisons between the processes and monotone functionals of the processes follow immediately from this construction. The stochastic comparisons are useful to obtain bounds for intractable systems. For example, the approach here yields bounds for queues with time-dependent arrival rates.

scholarly journals Measuring and Forecasting Volatility in Chinese Stock Market Using HAR-CJ-M Model

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Chuangxia Huang ◽  
Xu Gong ◽  
Xiaohong Chen ◽  
Fenghua Wen
Keyword(s):  
Stock Market ◽  
Sample Path ◽  
Realized Volatility ◽  
The Other ◽  
Chinese Stock Market ◽  
Momentum Effect ◽  
Forecasting Performance ◽  
The Future ◽  
Forecasting Volatility ◽  
Continuous Volatility

Basing on the Heterogeneous Autoregressive with Continuous volatility and Jumps model (HAR-CJ), converting the realized Volatility (RV) into the adjusted realized volatility (ARV), and making use of the influence of momentum effect on the volatility, a new model called HAR-CJ-M is developed in this paper. At the same time, we also address, in great detail, another two models (HAR-ARV, HAR-CJ). The applications of these models to Chinese stock market show that each of the continuous sample path variation, momentum effect, and ARV has a good forecasting performance on the future ARV, while the discontinuous jump variation has a poor forecasting performance. Moreover, the HAR-CJ-M model shows obviously better forecasting performance than the other two models in forecasting the future volatility in Chinese stock market.

scholarly journals Sample-Path Analysis of Single-Server Queue with Multiple Vacations

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Muhammad El-Taha
Keyword(s):  
Stochastic Process ◽  
Conservation Law ◽  
Sample Path ◽  
Single Server ◽  
Queueing Model ◽  
Single Server Queue ◽  
Sample Path Analysis ◽  
Multiple Vacation ◽  
Server Queue ◽  
Background Material

We a give deterministic (sample path) proof of a result that extends the Pollaczek-Khintchine formula for a multiple vacation single-server queueing model. We also give a conservation law for the same system with multiple classes. Our results are completely rigorous and hold under weaker assumptions than those given in the literature. We do not make stochastic assumptions, so the results hold almost surely on every sample path of the stochastic process that describes the system evolution. The article is self contained in that it gives a brief review of necessary background material.

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