# Questions tagged [wiener]

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### Integration on Wiener Process

How can I show that below equation holds ? $\int\limits_{0}^{t} f \left( s \right)W_s ds = W_t \int\limits_{0}^{t}f \left( s \right)ds - \int\limits_{0}^{t}\int\limits_{0}^{s} f\left( u \right)dudW_s$...
137 views

### Itô’s formula and Wiener process

The Wikipedia page on the formula https://en.wikipedia.org/wiki/It%C3%B4%27s_lemma and some textbooks I have looked at say we must assume that the relevant time-dependent function is over an Itô ...
373 views

### Discretization of Wiener process

The Wiener process $(W_t)$ is a continuous stochastic process that satisfies the following there conditions: $W_0 = 0$, the increments $\mathrm{d}W_t = W_{t + \mathrm{d}t} - W_t$ are normally ...
499 views

### Probability Density Function of a Wiener Process Minimum

Let $W_t$ be a standard Wiener process. Find the probability density function of $m_T = min_{t\in [0,T ]}W_t$. I know that it is based of the concept of the reflection principle, but I wasn't too ...
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### Algebraic Calculation of Wiener Process [closed]

What is the meaning of "Wiener Process does not support algebraic calculation hence we focused on it's increment"
764 views

### Reflection Principle

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\,\,\,\,...