위너 과정

노트

말뭉치

1. Given to the world by the American mathematician, philosopher, and founder of cybernetics Norbert Wiener, it is called, naturally enough, the Wiener process.
2. The next major concept to absorb on the path to understanding Wiener processes is that of the Gaussian process.
3. The Wiener process plays an important role in both pure and applied mathematics.
4. In pure mathematics, the Wiener process gave rise to the study of continuous time martingales.
5. The Wiener process has applications throughout the mathematical sciences.
6. A third characterisation is that the Wiener process has a spectral representation as a sine series whose coefficients are independent N(0, 1) random variables.
7. Wiener process (also called Brownian motion) is a stochastic process {Wt}t0+ indexed by nonnegative real numbers t with the following properties: (1) W0 = 0.
8. A Wiener process with initial value W0 = x is gotten by adding x to a standard Wiener process.
9. First, it explains, at least in part, why the Wiener process arises so commonly in nature.
10. It is advisable, when confronted with a problem about Wiener processes, to begin by reecting on how scaling might affect the answer.
11. The Wiener process plays an important role both in pure and applied mathematics.
12. The Wiener process can be constructed as the scaling limit of a random walk, or other discrete-time stochastic processes with stationary independent increments.
13. The Wiener measure is the probability law on the space of continuous functions g, with g(0) = 0, induced by the Wiener process.
14. Wiener process includes two parameters called drift rate \( \alpha \) that represent trend and degree of volatility \( \sigma \).
15. Figure above shows the comparison of Wiener process and random walk.
16. The Wiener process is using zero drift and the unit standard deviation to make it the same parameter with the random walk.
17. In general, Wiener process has much higher spread because of the factor of the square root of time.
18. This is why the Brownian motion is also called the Wiener process.
19. Solve Stochastic Dierential Equations with Stochastic Integral This chapter introduces the stochastic process (especially the Wiener process), Itos Lemma, and the stochastic intergral.

메타데이터

위키데이터

• ID : Q1056809

Spacy 패턴 목록

• [{'LOWER': 'wiener'}, {'LEMMA': 'process'}]