I am having some trouble working out $E\left[ \int_0^tg^2(\tau)dW_\tau \right]$. I don't even really know where to begin, I'm very new to Ito Calculus and any help or nudge in the right direction would be much appreciated.
2026-04-08 05:51:35.1775627495
What is the expectation of the Ito integral $\int_0^tg^2(\tau)dW_\tau$?
72 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in STATISTICS
- Given is $2$ dimensional random variable $(X,Y)$ with table. Determine the correlation between $X$ and $Y$
- Statistics based on empirical distribution
- Given $U,V \sim R(0,1)$. Determine covariance between $X = UV$ and $V$
- Fisher information of sufficient statistic
- Solving Equation with Euler's Number
- derive the expectation of exponential function $e^{-\left\Vert \mathbf{x} - V\mathbf{x}+\mathbf{a}\right\Vert^2}$ or its upper bound
- Determine the marginal distributions of $(T_1, T_2)$
- KL divergence between two multivariate Bernoulli distribution
- Given random variables $(T_1,T_2)$. Show that $T_1$ and $T_2$ are independent and exponentially distributed if..
- Probability of tossing marbles,covariance
Related Questions in STOCHASTIC-PROCESSES
- Interpreting stationary distribution $P_{\infty}(X,V)$ of a random process
- Probability being in the same state
- Random variables coincide
- Reference request for a lemma on the expected value of Hermitian polynomials of Gaussian random variables.
- Why does there exists a random variable $x^n(t,\omega')$ such that $x_{k_r}^n$ converges to it
- Compute the covariance of $W_t$ and $B_t=\int_0^t\mathrm{sgn}(W)dW$, for a Brownian motion $W$
- Why has $\sup_{s \in (0,t)} B_s$ the same distribution as $\sup_{s \in (0,t)} B_s-B_t$ for a Brownian motion $(B_t)_{t \geq 0}$?
- What is the name of the operation where a sequence of RV's form the parameters for the subsequent one?
- Markov property vs. transition function
- Variance of the integral of a stochastic process multiplied by a weighting function
Related Questions in EXPECTED-VALUE
- Show that $\operatorname{Cov}(X,X^2)=0$ if X is a continuous random variable with symmetric distribution around the origin
- prove that $E(Y) = 0$ if $X$ is a random variable and $Y = x- E(x)$
- Limit of the expectation in Galton-Watson-process using a Martingale
- Determine if an Estimator is Biased (Unusual Expectation Expression)
- Why are negative constants removed from variance?
- How to find $\mathbb{E}(X\mid\mathbf{1}_{X<Y})$ where $X,Y$ are i.i.d exponential variables?
- $X_1,X_2,X_3 \sim^{\text{i.i.d}} R(0,1)$. Find $E(\frac{X_1+X_2}{X_1+X_2+X_3})$
- How to calculate the conditional mean of $E(X\mid X<Y)$?
- Let X be a geometric random variable, show that $E[X(X-1)...(X-r+1)] = \frac{r!(1-p)^r}{p^r}$
- Taylor expansion of expectation in financial modelling problem
Related Questions in STOCHASTIC-CALCULUS
- Interpreting stationary distribution $P_{\infty}(X,V)$ of a random process
- Reference request for a lemma on the expected value of Hermitian polynomials of Gaussian random variables.
- Why does there exists a random variable $x^n(t,\omega')$ such that $x_{k_r}^n$ converges to it
- Compute the covariance of $W_t$ and $B_t=\int_0^t\mathrm{sgn}(W)dW$, for a Brownian motion $W$
- Mean and variance of $X:=(k-3)^2$ for $k\in\{1,\ldots,6\}$.
- 4th moment of a Wiener stochastic integral?
- Unsure how to calculate $dY_{t}$
- What techniques for proving that a stopping time is finite almost surely?
- Optional Stopping Theorem for martingales
- $dX_t=\alpha X_t \,dt + \sqrt{X_t} \,dW_t, $ with $X_0=x_0,\,\alpha,\sigma>0.$ Compute $E[X_t] $ and $E[Y]$ for $Y=\lim_{t\to\infty}e^{-\alpha t}X_t$
Related Questions in FINANCE
- Compute the net present value of this project in dependance of the interest rate p.
- Maximizing profit when demand is a power function
- How do I calculate if 2 stocks are negatively correlated?
- Why does the least risky portfolio have large weight on the eigenvectors with small eigenvalues?
- FM Actuary question, comparing interest rate and Discount rate
- Monthly effective interest rate to 6-month effective interest rate
- Annual interest rate compounded monthly to monthly effective interest rate
- Withdrawing monthly from a bank for 40 years
- PMT equation result
- Fair value of European Call
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?