Questions tagged [stochastic-approximation]
The stochastic-approximation tag has no usage guidance.
7
questions
1
vote
0
answers
91
views
Adiabatic elimination of "fast"/"velocity" variable
My question comes from section IV, part A of the paper titled Stochastic resonance. Specifically, their equation (4.1) states that, if we start with a Langevin equation of the form $$m\ddot{x} = -m\...
1
vote
0
answers
50
views
A semimartingale interpolation problem
This question is a direct extension of this one.
Let $(\Omega,\mathcal{F},(\mathcal{F}_t)_{t\geq 0},\mathbb{P})$ be a stochastic basis and let $N\in\mathbb{Z}^+$, $T>0$, $\{t_n\}_{n=1}^{N}$ be a ...
0
votes
1
answer
84
views
A martingale extension/interpolation problem
Let $(\Omega,\mathcal{F},(\mathcal{F}_t)_{t\geq 0},\mathbb{P})$ be a stochastic basis and let $N\in\mathbb{Z}^+$, $T>0$, $\{t_n\}_{n=1}^{N}$ be a partition of $[0,T]$ with $t_0=0,t_n<t_{n+1},t_N=...
2
votes
0
answers
71
views
The stochastic approximation algorithm of Robbins-Monro
I am reading A Stochastic Approximation Method by Herbert Robbins and Sutton Monro and have a question concerning their algorithm. In below, I will basically follow their construction but will change ...
3
votes
0
answers
96
views
Applications of products of random matrices
I'm studying the paper "Matrix concentration for products" and I'm trying to find simple applications of the inequalities for the expected value of the spectral norm of products of random ...
2
votes
0
answers
68
views
Minimizing $\int\lambda({\rm d}y)\frac{\left|g(y)-\frac{p(y)}c\lambda g\right|^2}{r((i,x),y)}$ with respect to discrete parameter $i$
Let $I\subseteq\mathbb N$ be finite and nonempty, $(E,\mathcal E,\lambda)$ be a $\sigma$-finite measure space, $$\lambda f:=\int f\:{\rm d}\lambda$$ for $\lambda$-integrable $f:E\to\mathbb R$, $p:E\to(...
1
vote
0
answers
74
views
Reference for the positive probability of convergence to a stable point of a stochastic approximation algorithm
Consider a stochastic approximation process with
$$x_{t+1} = x_t + \frac{1}{t} (g(x_t)+u_t)$$
where $(u_s)_s$ is a sequence of i.i.d. shocks.
Assume $g$ is Lipschitz, $u_t$ has finite variance, and ...