Questions tagged [wiener]

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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"
4
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2answers
501 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\,\,\,\,...
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3answers
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How to differentiate a brownian motion?

By definition a wiener process cannot be differentiated. But when we use Ito's lemma on $F = X^2$, where X is wiener process we have total change in $$dF = 2XdX + dt$$ How can we calculate $\...
4
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3answers
422 views

Show that $E[B_t|\mathscr{F}_s] = B_s$ for $B_t = W_t^3 - 3 t W_t$

Given prob space $(\Omega, \mathscr{F}, P)$ and a Wiener process $(W_t)_{t \geq 0}$, define filtration $\mathscr{F}_t = \sigma(W_u : u \leq t)$ Let $(B_t)_{t \geq 0}$ where $B_t = W_t^3 - 3tW_t$. ...
4
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3answers
349 views

Determine $E[W_p W_q W_r]$

Given prob space $(\Omega, \mathscr{F}, P)$ and a Wiener process $(W_t)_{t \geq 0}$, define filtration $\mathscr{F}_t = \sigma(W_u : u \leq t)$ Let 0 < p < q < r. Determine $E[W_p W_q W_r]$. ...
3
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3answers
1k views

How can the Wiener process be nowhere differentiable but still continuous?

Taking a class in financial derivatives (book we use is Tomas Bjork´s Arbitrage theory in continuous time) but can´t understand the exact meaning of how the Wiener process is defined. In the book one ...