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Results tagged with pr.probability
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user 42537
Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
1
vote
Question about characteristic function with independence assumption
To determine the distributions it is sufficient to have two vectors in $S^1$, with the first coordinate not having the same absolute value, and the assumptions of the Hamburger moment problem.
Claim …
- 271
8
votes
Markov processes lacking the Feller property
A trivial example. Let $E = [0,\infty)$. Consider the translation semigroup for $c >0$:
\begin{align} P_t f(x) &= f(x+ct),\, x >0, \\
P_t f(0) &= f(0).
\end{align}
So the particle moves to the right w …
- 271
2
votes
On the pathwise uniqueness of solutions of SDEs(Stochastic Differential Equations)
I do not provide a proof here, but I guess the answer to the question "Is it true that $P(\Omega_0)=0$" is NO. I will give an answer to a simpler, yet similar question which is inspired by a great art …
- 271
0
votes
Accepted
Determining the Fourier transform
An interesting article may be A sharp form of the Cramér-Wold theorem by Cuesta-Albertos, Fraiman and Ransford, which can be found here: klick
Their Theorem 3.1 states that under a moment condition a …
- 271
0
votes
Accepted
On the existence and uniqueness of solution to SPDE with nonlinear growth coefficients
Call the drift term $b(u) = u (K- u)$ and for simplicity set $K=1$. Consider the following space of functions:
$$C_{\text{tem}}(\mathbb{R},\mathbb{R}) = \{ f:\mathbb{R} \to \mathbb{R}:\, \sup_{x \in \ …
- 271