# Questions tagged [wienerprocess]

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### Regression of stochastic integral on Wiener process

This question is a follow-up from the following: conditional expectation of stochastic integral so I won't repeat myself regarding assumptions and notation. Using Brownian bridge approach, we know ...
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### Integral of Wiener process w.r.t. time

I have a doubt with regards to the calculation of the below integral- $\int_0^t W_sds$ where $W_s$ is the Wiener Process. This has been solved very ably in the following page. It turns out to be a ...
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### Integral of the OU (Ornstein Uhlenbeck) process conditioned on hitting a threshold value for the first time

Let say I have a zero-mean OU process as follows: $dX_t = -\alpha X_t + dW_t$ The process starts at $x_0 = 0%$ and I'm interested in the event in which the process hits the value $x_{\tau} = a$ for ...
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### Two Wiener process under same martingale measure Q

Let $W_1,$ $W_2$ be to Wiener processes under the martingale measure $Q$. What can be said about $dW_1*dW_2$? I know that $$(dW_i)^2=dt$$ but what about the case with two different wiener processes?
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### Geometric Brownian Motion: Why is the Wiener process multiplied by volatility?

Below is the stochastic differential equation of the Geometric Brownian Motion: $$dS_t = S_t \mu dt + S_t\sigma dW_t$$ My understanding of the Wiener process is that the volatility component of an ...
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Assume there are two stochastic processes: $dx_t = \alpha_1(x_t,t)dt + \beta_1(x_t,t)dW^1_t$ and $dy_t = \alpha_2(y_t,t)dt + \beta_2(y_t,t)dW^2_t$. Does $dW^1_t\times{dW^2_t} = 0$ imply that $\... 1answer 256 views ### On the reflection of a stochastic integral Let${(I_t)}_{t\geq 0}$be a stochastic integral defined by $$I_t=\int_{0}^{t}\theta_sdW_t,$$ where$W$is a standard Brownian motion defined on$(\Omega,\mathcal{F},{(\mathcal{F}_t)}_{t\geq 0},\...
I just came across this stochastic process (link): $dY_t = (a-bY_t)dt + c \sqrt{Y_t(1-Y_t)}dW_t$, where $dW_t$ is a Wiener Process. According to the author under certain conditions this process is ...