2019年12月7日 · Indeed, your expression is same as what I got after applying Ito isometry. I think the problem might have an error.

2020年1月2日 · From general (multi-dimensional) Ito-isometry, the two integrals are uncorrelated. Using approximations of F and G by simple functions, one can show uncorrelation probably pretty straight forward.

2020年12月29日 · where σt is a sufficiently regular deterministic function and Wt is a standard Wiener process (that is Wt ∼ N(0, t) with independent increments). It can be shown that Mt is martingale with distribution Mt ∼ N(0, Σt) where (Ito's isometry) I have defined the variance Σt …

2021年5月10日 · For Question 1, you absolutely can use Ito isometry. First, note that we can use integration by parts to obtain the formula: ∫1 0Wtdt = W1 − ∫1 0tdWt = ∫1 0(1 − t)dWt

2019年10月24日 · which is indeed an Ito integral and in this case a Gaussian r.v. with mean zero and variance given by Ito isometry.

Can I use Ito isometry to calculate Var(Yt) V a r (Y t) where Yt = ∫t+1 t BsdBs Y t = ∫ t t + 1 B s d B s and Bs B s is Brownian motion, in this way? Is my reasoning correct?

2021年4月5日 · I'm looking for a plain English explanation of Ito's integral. I don't need an exhaustive proof, derivation, etc. Just a simple ~this is effectively what it does and why it's better than a Riemann ...

2020年5月9日 · I am new to stochastic calculus and I'm still grappling with the concepts. Can someone please verify whether I am correct to solve my question this way: In my question, I need to calculate: \\begin{

2014年7月21日 · In most textbooks Ito's lemma is derived (on different levels of technicality depending on the intended audience) and then only the classic examples of Geometric Brownian motion and the Black-Scholes equation are given.

where πn is a sequence of partitions of [0, t] with mesh going to zero. Then ∫t0f(τ)dWτ is a sum of normal random variables and hence is normal. So all we need to do is calculate the mean and variance. Firstly: E(lim n → ∞ ∑ [ti − 1, ti] ∈ πnf(ti − 1)(Wti − Wti − 1)) = lim n → ∞∑ [ti − 1, ti] ∈ πnf(ti − 1)E(Wti − Wti − 1) = lim n → ∞∑ [ti − 1, ti ...