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Results tagged with stochastic-processes
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user 76238
A stochastic process is a collection of random variables usually indexed by a totally ordered set.
1
vote
1
answer
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Mixing the Ornstein-Uhlenbeck Process and Geometric Brownian Motion
The Ornstein-Uhlenbeck process with mean reversion level 0 is defined as follows:
$$dX_t=a X_t dt + \sigma_1 d W_{1t}. \tag{1} $$
Geometric Brownian motion is defined as follows:
$$dX_t= a X_t dt + …
- 211
1
vote
2
answers
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Understanding the limits of the Ito Process Defintion
I would like to understand what kind of stochastic process are Ito Processes. According to Kuo[p. 102] an Ito Process is a stochastic process of the form
$$dX_t=g(t)dt+f(t)dW(t),$$
where $W(t)$ is a …
- 211
7
votes
1
answer
810
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Solve SDE $dX_t=(c+\sigma_\zeta W'_t)X_tdt + \sigma_\epsilon dW_t$
I am trying to solve the following SDE
$$dX_t=(c+\sigma_\zeta W'_tX_t)dt + \sigma_\epsilon dW_t$$
$c\in \mathbb{R}$ is a constant, $X_t$ is a stochastic process, $\sigma_\zeta,\sigma_\epsilon \in \ma …
- 211