scholarly journals Time Step Rescaling Recovers Continuous-Time Dynamical Properties for Discrete-Time Langevin Integration of Nonequilibrium Systems

2014 ◽  
Vol 118 (24) ◽  
pp. 6466-6474 ◽  
Author(s):  
David A. Sivak ◽  
John D. Chodera ◽  
Gavin E. Crooks
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Nonequilibrium Systems ◽  
Time Step ◽  
Dynamical Properties

Hedging in discrete time under transaction costs and continuous-time limit

1999 ◽  
Vol 36 (1) ◽  
pp. 163-178 ◽  
Author(s):  
Pierre-F. Koehl ◽  
Huyên Pham ◽  
Nizar Touzi
Keyword(s):  
Transaction Costs ◽  
Discrete Time ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Risky Asset ◽  
Market Model ◽  
Upper And Lower Bounds ◽  
Time Step ◽  
Proportional Transaction Costs ◽  
Call Options

We consider a discrete-time financial market model with L1 risky asset price process subject to proportional transaction costs. In this general setting, using a dual martingale representation we provide sufficient conditions for the super-replication cost to coincide with the replication cost. Next, we study the convergence problem in a stationary binomial model as the time step tends to zero, keeping the proportional transaction costs fixed. We derive lower and upper bounds for the limit of the super-replication cost. In the case of European call options and for a unit initial holding in the risky asset, the upper and lower bounds are equal. This result also holds for the replication cost of European call options. This is evidence (but not a proof) against the common opinion that the replication cost is infinite in a continuous-time model.

Uniform-in-time transition from discrete dynamics to continuous dynamics in the Cucker–Smale flocking

2018 ◽  
Vol 28 (09) ◽  
pp. 1699-1735 ◽  
Author(s):  
Seung-Yeal Ha ◽  
Xiongtao Zhang
Keyword(s):  
Initial Data ◽  
Discrete Time ◽  
Continuous Time ◽  
Lyapunov Functional ◽  
Discrete Model ◽  
Stability Estimate ◽  
Functional Approach ◽  
Time Interval ◽  
Time Step ◽  
Time Model

We study a uniform-in-time convergence from the discrete-time (in short, discrete) Cucker–Smale (CS) model to the continuous-time CS model, which is valid for the whole time interval, as time-step tends to zero. Classical theory yields the convergence results which are valid only in any finite-time interval. Our uniform convergence estimate relies on two quantitative estimates “asymptotic flocking estimate” and “uniform[Formula: see text]-stability estimate with respect to initial data”. In the previous literature, most studies on the CS flocking have been devoted to the continuous-time model with general communication weights, whereas flocking estimates have been done for the discrete-time model with special network topologies such as the complete network with algebraically decaying communication weights and rooted leaderships. For the discrete CS model with a regular and algebraically decaying communication weight, asymptotic flocking estimate has been extensively studied in the previous literature. In contrast, for a general decaying communication weight, corresponding flocking dynamics has not been addressed in the literature due to the difficulty of extending the Lyapunov functional approach to the discrete model. In this paper, we present asymptotic flocking estimate for the discrete model using the Lyapunov functional approach. Moreover, we present a uniform [Formula: see text]-stability estimate of the solution for the discrete CS model with respect to initial data. We combine asymptotic flocking estimate and uniform stability to derive a uniform-in-time convergence from the discrete CS model to the continuous CS model, as time-step tends to zero.

Hedging in discrete time under transaction costs and continuous-time limit

1999 ◽  
Vol 36 (01) ◽  
pp. 163-178 ◽  
Author(s):  
Pierre-F. Koehl ◽  
Huyên Pham ◽  
Nizar Touzi
Keyword(s):  
Transaction Costs ◽  
Discrete Time ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Risky Asset ◽  
Market Model ◽  
Upper And Lower Bounds ◽  
Time Step ◽  
Proportional Transaction Costs ◽  
Call Options

We consider a discrete-time financial market model with L 1 risky asset price process subject to proportional transaction costs. In this general setting, using a dual martingale representation we provide sufficient conditions for the super-replication cost to coincide with the replication cost. Next, we study the convergence problem in a stationary binomial model as the time step tends to zero, keeping the proportional transaction costs fixed. We derive lower and upper bounds for the limit of the super-replication cost. In the case of European call options and for a unit initial holding in the risky asset, the upper and lower bounds are equal. This result also holds for the replication cost of European call options. This is evidence (but not a proof) against the common opinion that the replication cost is infinite in a continuous-time model.

scholarly journals Optimal measurement budget allocation for Kalman prediction over a finite time horizon by genetic algorithms

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Antoine Aspeel ◽  
Axel Legay ◽  
Raphaël M. Jungers ◽  
Benoit Macq
Keyword(s):  
Genetic Algorithm ◽  
Discrete Time ◽  
Continuous Time ◽  
Estimation Error ◽  
Budget Allocation ◽  
Finite Horizon ◽  
Time Step ◽  
Optimal Measurement ◽  
Discrete Time Dynamical System ◽  
The Impact

AbstractIn this paper, we address the problem of optimal measurement budget allocation to estimate the state of a linear discrete-time dynamical system over a finite horizon. More precisely, our aim is to select the measurement times in order to minimize the variance of the estimation error over a finite horizon. In addition, we investigate the closely related problem of finding a trade-off between number of measurements and signal to noise ratio.First, the optimal measurement budget allocation problem is reduced to a deterministic combinatorial program. Then, we propose a genetic algorithm implementing a count preserving crossover to solve it. On the theoretical side, we provide a one-dimensional analysis that indicates that the benefit of using irregular measurements grows when the system is unstable or when the process noise becomes important. Then, using the duality between estimation and control, we show that the problem of selecting optimal control times for a linear quadratic regulator can be reduced to our initial problem.Finally, numerical implementations demonstrate that using measurement times optimized by our genetic algorithm gives better estimate than regularly spaced measurements. Our method is applied to a discrete version of a continuous-time system and the impact of the discretization time step is studied. It reveals good convergence properties, showing that our method is well suited to both continuous-time and discrete-time setups.

Design of Programmable Wideband Low Pass Filter with Continuous-Time/Discrete-Time Hybrid Architecture

2017 ◽  
Vol E100.C (10) ◽  
pp. 858-865 ◽  
Author(s):  
Yohei MORISHITA ◽  
Koichi MIZUNO ◽  
Junji SATO ◽  
Koji TAKINAMI ◽  
Kazuaki TAKAHASHI
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Hybrid Architecture ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Low Pass

scholarly journals Time to Intervene: A Continuous-Time Approach to Network Analysis and Centrality

Psychometrika ◽  
2021 ◽  
Author(s):  
Oisín Ryan ◽  
Ellen L. Hamaker
Keyword(s):  
Network Analysis ◽  
Discrete Time ◽  
Continuous Time ◽  
Centrality Measures ◽  
Time Interval ◽  
Direct Effects ◽  
Network Approach ◽  
Var Models ◽  
Auto Regressive ◽  
Conceptual Shift

AbstractNetwork analysis of ESM data has become popular in clinical psychology. In this approach, discrete-time (DT) vector auto-regressive (VAR) models define the network structure with centrality measures used to identify intervention targets. However, VAR models suffer from time-interval dependency. Continuous-time (CT) models have been suggested as an alternative but require a conceptual shift, implying that DT-VAR parameters reflect total rather than direct effects. In this paper, we propose and illustrate a CT network approach using CT-VAR models. We define a new network representation and develop centrality measures which inform intervention targeting. This methodology is illustrated with an ESM dataset.

On quasi-stationary distributions in absorbing continuous-time finite Markov chains

1967 ◽  
Vol 4 (1) ◽  
pp. 192-196 ◽  
Author(s):  
J. N. Darroch ◽  
E. Seneta
Keyword(s):  
Markov Chains ◽  
Discrete Time ◽  
Continuous Time ◽  
Present Note ◽  
Time Parameter ◽  
Stationary Distributions ◽  
Finite State ◽  
Absorbing Markov Chains ◽  
Finite Markov Chains ◽  
Finite State Space

In a recent paper, the authors have discussed the concept of quasi-stationary distributions for absorbing Markov chains having a finite state space, with the further restriction of discrete time. The purpose of the present note is to summarize the analogous results when the time parameter is continuous.

MATLAB/SIMULINK-based high-level synthesis of discrete-time and continuous-time ΣΔ modulators

2004 ◽  
Author(s):  
J. Ruiz-Amaya ◽  
J.M. de la Rosa ◽  
F. Medeiro ◽  
F.V. Fernandez ◽  
R. del Rio ◽  
...  
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
High Level Synthesis ◽  
Matlab Simulink ◽  
High Level

Continuous-Time Versus Discrete-Time Point Process Models for Rainfall Occurrence Series

1986 ◽  
Vol 22 (4) ◽  
pp. 531-542 ◽  
Author(s):  
Efi Foufoula-Georgiou ◽  
Dennis P. Lettenmaier
Keyword(s):  
Point Process ◽  
Discrete Time ◽  
Continuous Time ◽  
Process Models ◽  
Rainfall Occurrence ◽  
Point Process Models ◽  
Time Point
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