2,210 reputation
1517
bio website
location
age
visits member for 3 years, 10 months
seen 57 mins ago

3h
awarded  Explainer
1d
comment Martingality Theorem: Solving expectation of a stochastic integral
@ Innombrabre : I think your argument is not conclusive as claimed, the true fact (that you have shown) that $\lim_{n\to\infty}\mathbf{P}(\tau_n<T)=0$ is not enough to conclude directly by localization. This is true for any continuous non explosive strict loc mart. What needs to be shown is that $E[<V>_t]<\infty$ (maybe by localization). The fact that $\int_0^t\sigma e^{-k(t-u)}\sqrt{V_u}dW_u$ is a martingale is usually shown using that the CIR process is a time-changed Besel Square proc which in turn has moments of all orders. Regards
Aug
25
comment Explicit solution SDE?
@Math Girl : The last comment of Chinny84 is very strong because if a solution exists it tells you that is has to be a Brownian motion tank's to Lévy's theorem on continuous local martingale, which is quite explicit in my opinion. Best regards
Aug
6
comment Independence of two processes
@ DEW: You have too impose severe constraints on your coefficients for this to be true. For example take $a(x)=p(x)=0, \forall x\in \mathbb{R}$ and $b_1(x)=q_1(x)=1, \forall x\in \mathbb{R}$ and $b_2(x)=q_2(x)=0, \forall x\in \mathbb{R}$ then $X=Y$. Best regards
Aug
4
comment exercise 1.21 of chapter 1 of Revuz and Yor's
Hi, I think that if you post your solution on what you have done so far, it might attract more interest from the community (moreover your solution will be checked). Best regards.
Jul
2
awarded  Curious
Jun
27
reviewed Approve suggested edit on How to prove that a limit is wrong using Epsilon-Delta definition?
Jun
27
reviewed Approve suggested edit on upper bound for error in multivariable differential
May
28
reviewed Approve suggested edit on Solving exponential equations using logarithms
May
23
comment Kolmogorov theorem
@kaciou : For a full proof of this theorem you should take a look à Karatzas and Shreve book "Brownian Motion and Stochastic Calculus". Regards
May
23
reviewed Approve suggested edit on Boundary Value Problem$ 5U_x+2U_y=(x-y)^2$
May
23
reviewed Approve suggested edit on Planar graph proof
May
16
comment Combination of Wiener Processes
You should note first that the law of the Euclidian norm of a multidimensional Brownian Motion is invariant under rotation and second try to determine this law.Best regards
May
9
reviewed Approve suggested edit on A problem about ideals and isomorphism
May
9
reviewed Approve suggested edit on Random convex shapes containing a ball
May
6
reviewed Reject suggested edit on Choosing a password with constraints
May
2
reviewed Approve suggested edit on Is this exponential equation solvable? natural logarithms, exponential
May
2
reviewed Approve suggested edit on Theorem of Galvin, Mycielski and Solovay
Apr
30
reviewed Approve suggested edit on Roots of a cubic expression and arithmetic progression
Apr
26
reviewed Approve suggested edit on Uniform convergence of sequence of partial sums.Help please