Level crossings of a two-parameter random walk

Zeros of a two-parameter random walk∗

We prove that the number γN of the zeros of a two-parameter simple random walk in its first N × N time steps is almost surely equal to N as N →∞. This is in contrast with our earlier joint effort with Z. Shi [4]; that work shows that the number of zero crossings in the first N × N time steps is N (3/2)+o(1) as N → ∞. We prove also that the number of zeros on the diagonal in the first N time ste...

On the average number of sharp crossings of certain Gaussian random polynomials

Distribution of the spacing between two adjacent avoided crossings.

We consider the frequency at which avoided crossings appear in an energy-level structure when an external field is applied to a quantum chaotic system. The distribution of the spacing in the parameter between two adjacent avoided crossings is investigated. Using a random matrix model, we find that the distribution of these spacings is well fitted by a power-law distribution for small spacings. ...

Recurrence of Random Walk Traces

We show that the edges crossed by a random walk in a network form a recurrent graph a.s. In fact, the same is true when those edges are weighted by the number of crossings. §

A Fuzzy Random Walk Technique to Forecasting Volatility of Iran Stock Exchange Index

Study of volatility has been considered by the academics and decision makers dur-ing two last decades. First since the volatility has been a risk criterion it has been used by many decision makers and activists in capital market. Over the years it has been of more importance because of the effect of volatility on economy and capital markets stability for stocks, bonds, and foreign exchange mark...