# Tagged Questions

stochastic processes is a collection of random variables representing the evolution of some system of random values over time.

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### Stochastic process with non-independent increments

All stochastic process I see always have independent increments. It is true for: standard brownian motion geometric brownian motion (?) Ornstein Uhlenbeck (?) in general, Levy process etc. What ...
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### justification of square root process

In finance, many stochastic processes $X(t)$ are defined via $$dX = \text{(some drift term)} dt + \sigma X^\gamma dW_t$$ with $\gamma = 1/2$ (for instance the Heston model ...
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I'm looking for some reference on how to calibrate a non-mean-reverting Ornstein-Uhlenbeck process to historical data using MLE or OLS. The model has the following SDE: $d\lambda(t)=a\lambda(t)dt+\... 0answers 123 views ### Is there a countably infinite Sigma-Algebra? Why? Assume$\,\mathcal{F}$be a nonempty collection of subsets of$\Omega$.$\,\mathcal{F}$is called a$\sigma$-Algebra whenever if$A\in\mathcal{F}$then$A^c\in\mathcal{F}$, and if$A_1,A_2,...\in\...
Let $(\Omega,\mathcal{F},P)$ be a probability space and $\{W_t ∶ t ≥ 0\}$ be a standard Wiener process. By setting $\tau$ as a stopping time and defining \begin{align} W^*(t)=\Big\{\matrix{W_t\,\,\,\,...