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# All Questions

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### Convergence of SDEs

Suppose that $\{a_n(x)\}_{n \in \mathbb{N}}$ is a sequence of real-valued Lipschitz functions with domain $\mathbb{R}^d$, which converges $m$-a.e. to a Lipschitz function $a$. Suppose that $b$ is a ...
82 views

### Convergence of function of stochastic processes

Let $X_t$ be a fixed cadlag semi-martingale and $J_n$ be a fixed sequence of functions from $\mathbb{R}^d$ to $\mathbb{R}$ which are twice continuously differentiable. If $J_n$ converge pointwise to ...
169 views

### Superlinear Convergence of a Markov Chain

Suppose that we have a Markov process $\{Z_t\}_{t=0}^\infty$, where $Z_t \geq 0$ for any $t$. Assume that, conditioning on $Z_t = z_t$, we have $\mathbb{E}\{Z_{t+1}|Z_t = z_t\} \leq \kappa z_t^2$. ...
374 views

### Monotone convergence theorem for stochastic integrals

I was wondering if there exists an equivalent of a monotone convergence theorem for stochastic integrals. I looked into plenty of books and papers, but I haven't found anything useful. I would expect ...
196 views

### Convergence of an inhomogeneous markov chain

A markov chain is defined as $X_t=F(X_{t-1})X_{t-1}$, where $X_t$ and $X_{t-1}$ are both vector. So the transition matrix depends on the current states. I want to show that for any given initial ...
190 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 ...
250 views

### Convergence of an implicitly defined sequence of random variables

Let $\{X_n\}_{n\ge 1}$ be a sequence of independent identically distributed Poisson random variables with mean $\lambda^*$. Consider a sequence of random variables $\{\hat{\lambda}_{n}\}_{n\ge 1}$ ...
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148 views

### Eigenvalues of matrix products [closed]

Hi my problem is with row stochastic matrices. Its known that if we keep multiplying this row stochastic matrices, we will get a rank one row stochastic matrix. Rank one means that all the rows has ...

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