# Questions tagged [stochastic-calculus]

A branch of mathematics that operates on stochastic processes.

428 questions
Filter by
Sorted by
Tagged with
887 views

176 views

119 views

### What is the easiest way to learn Option pricing with PDE?

I was reading about Ito's formula and Girsanov theorem, but I am still struggling to grasp how in reality these are combined to compute the price of an option. What are the main source to understand ...
587 views

### Ito's Lemma: Multiplication Rule

I have a conceptual question about Ito's lemma, in particular, the multiplication. Ito's multiplication rule states, that multiplying dt by itself or by dx (the stochastic differential) equals zero. ...
482 views

### How to express the volatility of two correlated Ito processes $Wt_1, Wt_2$ expressed in terms of $W_t$?

Having two correlated Ito processes ($W_t^1$ and $W_t^2$ are correlated Brownian motions with correlation $\rho$) $dX_{t} =\mu_{1} dt + \sigma_1 dWt_1$ $dY_{t} = \mu_{2} dt + \sigma_2 dWt_2$ ...
2k views

### How to prove that $X_s=\int^s_0 f(u)dW_u$ is independant from $X_t-X_s$
I am asked to prove that $X_s$ and $X_t-X_s$ are independant for $s<t$ then $$X_t=\int^t_0f(u)dW_u$$ for a deterministic function $f$ and brownian motion $W_t$. For the proof I am giving a hint to ...