I need to find $D\int_{0}^{t} N_{s}dW_{s}$, where $N_{s}$ is Poisson process and $N_{s}$ and $W_{s}$ are independent. How can i do it?
2026-03-27 15:08:57.1774624137
Integral Ito (stohastic integral) of Poisson process
41 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in PROBABILITY
- How to prove $\lim_{n \rightarrow\infty} e^{-n}\sum_{k=0}^{n}\frac{n^k}{k!} = \frac{1}{2}$?
- Is this a commonly known paradox?
- What's $P(A_1\cap A_2\cap A_3\cap A_4) $?
- Prove or disprove the following inequality
- Another application of the Central Limit Theorem
- Given is $2$ dimensional random variable $(X,Y)$ with table. Determine the correlation between $X$ and $Y$
- A random point $(a,b)$ is uniformly distributed in a unit square $K=[(u,v):0<u<1,0<v<1]$
- proving Kochen-Stone lemma...
- Solution Check. (Probability)
- Interpreting stationary distribution $P_{\infty}(X,V)$ of a random process
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 STOCHASTIC-INTEGRALS
- Meaning of a double integral
- 4th moment of a Wiener stochastic integral?
- Cross Variation of stochatic integrals
- Stochastic proof variance
- Solving of enhanced Hull-White $dX_t = \frac{e^t-X_t}{t-2}dt + tdW_t$
- Calculating $E[exp(\int_0^T W_s dW_s)]$?
- Applying Ito's formula on a $C^1$ only differentiable function yielding a martingale
- what does it mean by those equations of random process?
- Why aren't the sample paths of this stochastic process defined?
- Is the solution to this (simple) Stochastic Differential Equation unique?
Related Questions in POISSON-PROCESS
- Meaning of a double integral
- planar Poisson line process & angles of inclination
- In the Poisson process $N,$ find $\operatorname E[2^{N(t)}e^{-\lambda t} \mid N(s) = k]$ and $\operatorname{Var}(N(t) \mid N(s) = k)$.
- Probability Bookings in a Hotel
- Fitting Count Data with Poisson & NBD
- Expected value mixed poisson process
- Convergence of iid random variables to a poisson process
- Poisson process - 2D
- To prove that $X(t) = N(t+L) - N(t) , L > 0$ is Covariance stationary given $\{N(t) | t \geq 0\}$ is a Poisson Process.
- Poisson point process characterized by inter-arrival times
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?