A continuous-time extension of welch~s lower bound on total squared correlation

2005 ◽  
Author(s):  
Joon Ho Cho
Keyword(s):  
Lower Bound ◽  
Continuous Time ◽  
Time Extension

scholarly journals Information design and sequential screening with ex post participation constraint

2020 ◽  
Vol 15 (1) ◽  
pp. 319-359 ◽  
Author(s):  
Tibor Heumann
Keyword(s):  
Lower Bound ◽  
Continuous Time ◽  
Information Design ◽  
Agent Model ◽  
Optimal Mechanism ◽  
Sequential Screening ◽  
Ex Post ◽  
Opt Out ◽  
Principal Agent Model ◽  
Participation Constraint

We study a principal–agent model. The parties are symmetrically informed at first; the principal then designs the process by which the agent learns his type and, concurrently, the screening mechanism. Because the agent can opt out of the mechanism ex post, it must leave him with nonnegative rents ex post. We characterize the profit‐maximizing mechanism. In that optimal mechanism, learning proceeds in continuous time and, at each moment, the agent learns a lower bound on his type. For each type, there is one of two possible outcomes: the type is allocated the efficient quantity or is left with zero rents ex post.

On a continuous time extension of Feller's Lemma

1971 ◽  
Vol 17 (3) ◽  
pp. 220-226 ◽  
Author(s):  
N. U. Prabhu ◽  
Michael Rubinovitch
Keyword(s):  
Continuous Time ◽  
Time Extension

scholarly journals An Exponential Continuous-Time GARCH Process

2007 ◽  
Vol 44 (04) ◽  
pp. 960-976 ◽  
Author(s):  
Stephan Haug ◽  
Claudia Czado
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Leverage Effect ◽  
New Model ◽  
Time Extension ◽  
Garch Process

In this paper we introduce an exponential continuous-time GARCH(p, q) process. It is defined in such a way that it is a continuous-time extension of the discrete-time EGARCH(p, q) process. We investigate stationarity, mixing, and moment properties of the new model. An instantaneous leverage effect can be shown for the exponential continuous-time GARCH(p, p) model.

scholarly journals On the achievable rate of bandlimited continuous-time AWGN channels with 1-bit output quantization

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sandra Bender ◽  
Meik Dörpinghaus ◽  
Gerhard P. Fettweis
Keyword(s):  
Lower Bound ◽  
Mutual Information ◽  
Gaussian Noise ◽  
Continuous Time ◽  
Additive White Gaussian Noise ◽  
White Gaussian Noise ◽  
Information Rate ◽  
Achievable Rate ◽  
Zero Crossing ◽  
Lower Bounding

AbstractWe consider a real continuous-time bandlimited additive white Gaussian noise channel with 1-bit output quantization. On such a channel the information is carried by the temporal distances of the zero-crossings of the transmit signal. We derive an approximate lower bound on the capacity by lower-bounding the mutual information rate for input signals with exponentially distributed zero-crossing distances, sine-shaped transition waveform, and an average power constraint. The focus is on the behavior in the mid-to-high signal-to-noise ratio (SNR) regime above 10 dB. For hard bandlimited channels, the lower bound on the mutual information rate saturates with the SNR growing to infinity. For a given SNR the loss with respect to the unquantized additive white Gaussian noise channel solely depends on the ratio of channel bandwidth and the rate parameter of the exponential distribution. We complement those findings with an approximate upper bound on the mutual information rate for the specific signaling scheme. We show that both bounds are close in the SNR domain of approximately 10–20 dB.

Optimal Sampled-Data Reconstruction of Stochastic Signals With Preview

2003 ◽  
Vol 125 (2) ◽  
pp. 224-228 ◽  
Author(s):  
K. Yu. Polyakov ◽  
E. N. Rosenwasser ◽  
B. P. Lampe
Keyword(s):  
Lower Bound ◽  
Continuous Time ◽  
Additive Noise ◽  
Signal Reconstruction ◽  
Sampling Period ◽  
Time Signal ◽  
Data Reconstruction ◽  
Sampled Data ◽  
Rigorous Solution ◽  
The Cost

The problem of H2-optimal reconstruction of a continuous-time signal using a stable sampled-data filter is considered. The signal is corrupted by additive noise and is measured with preview of τ, i.e., it is known in advance over the interval τ. This problem is equivalent to delayed signal reconstruction. A rigorous solution of the problem is presented on the basis of the parametric transfer function approach. Explicit expressions are given for the order of the optimal filter. A lower bound is obtained for the cost function for τ→∞, and it is shown that this bound depends on the ratio of the preview interval to the sampling period.

scholarly journals An Exponential Continuous-Time GARCH Process

2007 ◽  
Vol 44 (4) ◽  
pp. 960-976 ◽  
Author(s):  
Stephan Haug ◽  
Claudia Czado
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Leverage Effect ◽  
New Model ◽  
Time Extension ◽  
Garch Process

In this paper we introduce an exponential continuous-time GARCH(p, q) process. It is defined in such a way that it is a continuous-time extension of the discrete-time EGARCH(p, q) process. We investigate stationarity, mixing, and moment properties of the new model. An instantaneous leverage effect can be shown for the exponential continuous-time GARCH(p, p) model.

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