China
Africa
Explore chapters and articles related to this topic
What Is Amplification?
Published in Travis S. Taylor, Introduction to Laser Science and Engineering, 2019
Another type of noise that will be of great importance to laser scientists and engineers is the so-called shot noise. This type of noise was first discovered in 1918 by Walter Schottky while studying current signals in vacuum tubes. Hence, it is sometimes (not as often as it should be) referred to as Schottky noise. It is also sometimes called Poisson noise because it can be modeled as a Poisson random measure or process. Schottky discovered that when a signal was generated by discrete phenomena like electrons or photons and if the measurement time of that signal was on a similar order of magnitude as the discrete particle arrival times then there might arise an error in the signal’s measurement.
Quantum Filtering in Robotics, Information, Feynman Path Integrals, Levy Noise, Haar Measure on Groups, Gravity and Robots, Canonical Quantum Gravity, Langevin Equation, Antenna Current in a Field Dependent Medium
Published in Harish Parthasarathy, Electromagnetics, Control and Robotics, 2023
N(t, dξ) ≃ Poisson random measure ∫[0,t]xXf(s,ξ)N(ds,dξ)≃Compoundprocess
Bayesian Nonparametric Mixture Models
Published in Sylvia Frühwirth-Schnatter, Gilles Celeux, Christian P. Robert, Handbook of Mixture Analysis, 2019
Here we used that a priorip(θk⋆)=H0(θk⋆). This follows from the stick-breaking definition of the DP random measure. The posterior p(θk⋆|z,y) is simply the posterior on θk⋆ in a parametric model with prior H0(θk⋆) and sampling model p(yi|θk⋆), restricted to data yi, i ∈ Ck.
Robust optimal asset–liability management with delay and ambiguity aversion in a jump-diffusion market
Published in International Journal of Control, 2022
For convenience, we denote . Then it is easy to see that . Plugging (4) into (3), we obtain where and . For convenience, we use the Poisson random measure on to describe the compound Poisson process as and the compensator of the random measure is given by . Therefore, the compensated measure of Poisson random measure is Then, the dynamic of wealth process is equivalent to and the initial condition is the information about for . That is the investor is endowed with the initial wealth x at time point and do not start the businesses until the time 0.
Robust equilibrium strategy for DC pension plan with the return of premiums clauses in a jump-diffusion model
Published in Optimization, 2023
For each , , a real-valued process is defined as By the definition of , we know that is a martingale under . For each , there exists a progressively measurable process such that According to Girsanov's Theorem, under the alternative measure , the stochastic process is also a one-dimensional standard Brownian motion, i.e. and Poisson process becomes with intensity . For ease of tractability and interpretation, we assume that the distribution of jump is known and restricted to the same under and . Furthermore, the dynamics of the wealth process (8) under can be rewritten as where is a Poisson random measure under probability measure .
Interaction event network modeling based on temporal point process
Published in IISE Transactions, 2022
For a given series of interaction events we aim to model the dynamics of these interaction events by explicitly expressing the rate of events through temporal point processes. A one-dimensional temporal point process is a random measure that maps each Borel set on into a positive integer. Intuitively, we use to represent the number of points (events) during the time period (a, b), where N(t) is a counting process.