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A simple procedure to simulate multifractional Brownian motion paths

The fractional Brownian motions you generate must not be independent. They are generated from the same Gaussian field $(B_H(t))_{(H,t) \in [a,b] \times \mathbb{R}}$ and there exists a dependence ...

Is every compound Poisson distribution a mixed Poisson distribution?

(This answer considers mixed/compound Poisson processes instead of mixed/compound Poisson distributions.) I think that the only processes that are mixed Poisson and compound Poisson are ordinary ...
• 91

M/G/1 queue as a Markov renewal process: one-step transition probabilities

Case 1: leaving behind at least one job Suppose first that when job $n - 1$ departs, it leaves behind at least one other job, meaning $I_{n - 1} = i \geq 1$. Then job $n$ is already in the system when ...
• 91
1 vote

Law of OU process with time-dependent dynamics

As (assuming $\Sigma\in L^2([0,\infty))$ $$m_t=\mathbb{E}[X_t] = x + \int_0^t [M_s^1+M_s^2\mathbb{E}[X_s]] ds$$ by the fundamental theorem of calculus, the right hand side is differentiable in $t$, ...
• 105

Short time limits for SDE

No, for example, take $dX_t = 2 dB_t$. By the reflection principle the conditioned process is symmetric around 1, but $Y_1 = 2$.
• 656

Connection between invariant measure and positive recurrence for continuum state space markov chain

Yes, let's assume that sup (which I think should be in the denominator in the last expression) is finite, as otherwise it is always true. Suppose it is bounded by A, the each return time is also ...
• 656
Accepted

Large noise limit for SDE with general volatility coefficients

The answer is no, as can be seen in the case $\sigma(u) = u$, so that $X_t = \exp(W_t - t/2)$. For the result to be true, Markov's inequality implies that the law of $W$, conditional on $A_M$, would ...
• 7,739
Accepted

1 vote
Accepted

Using gradient descent in probability case

Lets first assume $\zeta_i=0$ and ask the following: under which conditions $w^*$ is a stable fixed point? If it's not a stable fixed point for noise-free case, then you won't end up with a fixed ...
• 2,152
1 vote

Step in proof of Itô formula

I believe you can condition on $F_0$. Under the regular conditional probability induced by $F_0$, $a_0$ and $b_0$ are deterministic, and of course $w$ is stil a Brownian motion. Then you can apply the ...
• 1,207