scholarly journals A note on cash-in-advance constraints in continuous time

2021 ◽  
Author(s):  
Eric Kam
Keyword(s):  
Steady State ◽  
Continuous Time ◽  
Time Transformations ◽  
Cash In Advance

This paper demonstrates a robust proof of the continuous-time transformations of Stockman's cash-in-advance constraints. When the constraint applies to consumption and capital purchases, monetary growth lowers steady state consumption and capital. When the constraint applies only to consumption purchases, monetary growth is superneutral.

scholarly journals A note on cash-in-advance constraints in continuous time

2021 ◽  
Author(s):  
Eric Kam
Keyword(s):  
Steady State ◽  
Continuous Time ◽  
Time Transformations ◽  
Cash In Advance

This paper demonstrates a robust proof of the continuous-time transformations of Stockman's cash-in-advance constraints. When the constraint applies to consumption and capital purchases, monetary growth lowers steady state consumption and capital. When the constraint applies only to consumption purchases, monetary growth is superneutral.

scholarly journals Stability and moment bounds under utility-maximising service allocations: Finite and infinite networks

2020 ◽  
Vol 52 (2) ◽  
pp. 463-490
Author(s):  
Seva Shneer ◽  
Alexander Stolyar
Keyword(s):  
Steady State ◽  
Wide Class ◽  
Continuous Time ◽  
Service Rate ◽  
Fluid Limit ◽  
Natural Conditions ◽  
Infinite Systems ◽  
Moment Bounds ◽  
Infinite Networks ◽  
State Moment

AbstractWe study networks of interacting queues governed by utility-maximising service-rate allocations in both discrete and continuous time. For finite networks we establish stability and some steady-state moment bounds under natural conditions and rather weak assumptions on utility functions. These results are obtained using direct applications of Lyapunov–Foster-type criteria, and apply to a wide class of systems, including those for which fluid-limit-based approaches are not applicable. We then establish stability and some steady-state moment bounds for two classes of infinite networks, with single-hop and multi-hop message routes. These results are proved by considering the infinite systems as limits of their truncated finite versions. The uniform moment bounds for the finite networks play a key role in these limit transitions.

On the GIX/G/∞ system

1990 ◽  
Vol 27 (3) ◽  
pp. 671-683 ◽  
Author(s):  
L. Liu ◽  
B. R. K. Kashyap ◽  
J. G. C. Templeton
Keyword(s):  
Steady State ◽  
Shot Noise ◽  
Continuous Time ◽  
Transient State ◽  
System Size ◽  
Noise Process ◽  
Shot Noise Process ◽  
Special Cases

By using a shot noise process, general results on system size in continuous time are given both in transient state and in steady state with discussion on some interesting results concerning special cases. System size before arrivals is also discussed.

On the GIX/G/∞ system

1990 ◽  
Vol 27 (03) ◽  
pp. 671-683 ◽  
Author(s):  
L. Liu ◽  
B. R. K. Kashyap ◽  
J. G. C. Templeton
Keyword(s):  
Steady State ◽  
Shot Noise ◽  
Continuous Time ◽  
Transient State ◽  
System Size ◽  
Noise Process ◽  
Shot Noise Process ◽  
Special Cases

By using a shot noise process, general results on system size in continuous time are given both in transient state and in steady state with discussion on some interesting results concerning special cases. System size before arrivals is also discussed.

Discrete Versus Continuous Time in an Endogenous Growth Model with Durable Consumption

2014 ◽  
Vol 2 (3-4) ◽  
pp. 67-75 ◽  
Author(s):  
Manuel A. Gómez
Keyword(s):  
Steady State ◽  
Endogenous Growth ◽  
Growth Model ◽  
Continuous Time ◽  
Continuous Variable ◽  
Continuous Time Model ◽  
Time Model ◽  
Durable Consumption ◽  
Monotonic Convergence ◽  
Endogenous Growth Model

AbstractThe choice of time as a discrete or continuous variable may radically affect the stability of equilibrium in an endogenous growth model with durable consumption. In the continuous-time model the steady state is locally saddle-path stable with monotonic convergence. However, in the discrete-time model the steady state may be unstable or saddle-path stable with monotonic or oscillatory convergence.

Some explicit formulas for the steady-state behavior of the queue with semi-Markovian service times

1977 ◽  
Vol 9 (1) ◽  
pp. 141-157 ◽  
Author(s):  
Marcel F. Neuts
Keyword(s):  
Steady State ◽  
Continuous Time ◽  
Explicit Formulas ◽  
State Behavior ◽  
Virtual Waiting Time ◽  
Poisson Arrivals ◽  
Queue Lengths ◽  
The Mean ◽  
Service Times ◽  
Recursive Matrix

This paper discusses a number of explicit formulas for the steady-state features of the queue with Poisson arrivals in groups of random sizes and semi-Markovian service times. Computationally useful formulas for the expected duration of the various busy periods, for the mean numbers of customers served during them, as well as for the lower order moments of the queue lengths, both in discrete and in continuous time, and of the virtual waiting time are obtained. The formulas are recursive matrix expressions, which generalize the analogous but much simpler results for the classical M/G/1 model.

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