All Questions
12 questions with no upvoted or accepted answers
5
votes
0
answers
1k
views
Asymptotic behavior of row sums in 2-d array of random variables
Set-up. Let $f : \mathbb{N} \to \mathbb{N}$ be increasing. For each $m \in [0,1]$, consider an infinite two-dimensional array of random variables, where row $n$ has $f(n)$ variables:
$B^m_{1,1}$ $B^...
- 61
3
votes
0
answers
136
views
An integral involving Levy process with no positive jumps
Let $L_t$ be a Levy process that has no positive jumps, but is not strictly decreasing, i.e
$$
L_t = \gamma t + \sigma B_t + J_t,
$$
where $B_t$ is a Brownian motion, $J_t$ is a pure jump process with ...
- 103
2
votes
0
answers
175
views
Representing a continuous time-inhomogeneous Markov chain by a stochastic integral
I am interested in the following mean-field model introduced in the reference below:
There are $N$ particles. At each instant of time, a particle's state is a particular value taken from the finite ...
- 31
2
votes
0
answers
207
views
markov processes and ergodic theory
For an ergodic Markov Chain
$$
\frac{1}{N}\sum_{i=1}^n f(X_i) \rightarrow E_\pi[f]
$$
where $\pi$ is the invariant distribution. I am also dealing with a Markovian process (a state space model to ...
- 169
2
votes
0
answers
199
views
CLT for a Markov Renewal Process
Suppose $(X,T)=\{(X_n,T_n)\}_{n\geq0}$ is a Markov renewal process, where $X$ is a finite-state, discrete-time Markov chain with state space $\{1,2,...,R\}$. $T$ is the additive component, more ...
- 41
1
vote
0
answers
55
views
Limit process of a sequence of Gaussian variables on mesh grid going to zero
Consider the interval $[0,1]$ and a partition $\mathscr{P}_n = \{ [t_i,t_{i+1}), \, i=1,\ldots,N_n \, : \, 0=t_0 < \ldots < t_{N_n} = 1\}$. Suppose that for all $i$ and $t \in [t_i,t_{i+1})$, we ...
- 141
1
vote
0
answers
36
views
Uniform distribution as argument for copula likelihood
I am reading a well-known paper about copulas by Chen and Fan (2006). Specifically, Proposition 4.2 (see attached), in which all the arguments are uniform $U_{t-1}, U_t$. However, when the copula is ...
- 33
1
vote
0
answers
57
views
Convergence of stochastic linear recurrences
Suppose that $\zeta_t$ is a univariate, stationary stochastic process ($t\in\mathbb{N}^+$).
Let $x_0\in\mathbb{R}^n$, and let $f:\mathbb{R}\rightarrow\mathbb{R}^{n\times n}$ be a continuously ...
- 183
1
vote
0
answers
61
views
Convergence of empirical measure to Mc-Kean Vlasov equation for mean-field model with jumps
I am interested in the following mean-field model introduced in the reference below:
There are $N$ particles. At each instant of time, a particle's state is a particular value taken from the finite ...
- 31
1
vote
1
answer
335
views
Finding a connection between two types of convergence
Please, help me find connections between two types of convergence:
Let $\{X_n\}_{n\ge1}: (\Omega,F,P) \rightarrow (\mathbb{R},Bor)$ be a sequence of r.v., there are two convergences:
1) $X_n \...
- 31
0
votes
0
answers
74
views
Convergence of stochastic process $X_n$
Consider the discrete time random process $X_n,n\in \mathbb N$, with
$$X_{n+1}=(1-K)\cdot X_n+K\cdot\frac{G_n}{c}\cdot X_n$$
where $G_n$ is a random variable with expectation $\mathbb E[G_n\mid X_n]=\...
- 5
0
votes
0
answers
123
views
Tightness of a uniformly bounded sequence of functions integrated with respect to a semimartingale
I am reading this paper by Jacod, Jakubowski and Mémin. In the proof of Theorem 1.3 the authors define, for each $n\geq1$ the function $\phi_n$ by
$\quad\phi_n(s)=i+1-ns,\quad\text{if } \frac{i}{n}&...
- 101