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Kotlarski (1978) proved a result on identification of the distributions of independent random variables $X,Y$ and $Z$ from the joint distribution of the bivariate random vector $(U,V)$ where $(U,V)= (\max(X,Z),\max(Y,Z)).$ We extend this result to the case $(U,V)=(\max(X,aZ_1,bZ_2),\max(Y,cZ_1,dZ_2))$ where $X,Y,Z_1,Z_2$ are independent or max-independent random variables, $Z_1$ and $Z_2$ are identically distributed and $a,b,c,d$ are known positive constants.

We investigate the valuation of the bid and ask prices for European option under the mixed fractional Brownian motion environment in the presence of superimposed jumps by an independent Poisson process.

We study the problem of nonparametric estimation of the linear multiplier function $\theta(t)$ for processes satisfying stochastic differential equations of the type $$dX_t=\theta(t)X_tdt+\epsilon dW_t^{H,K}, X_0=x_0,0\leq t \leq T$$ where $\{W_t^{H,K}, t \geq 0\}$ is a bifractional Brownian motion with known parameters $H\in (0,1), K\in (0,1]$ and $HK\in (\frac{1}{2},1).$ We investigate the asymptotic behaviour of the estimator of the unknown function $\theta(t)$ as $\epsilon \rightarrow 0.$

We derive some maximal inequalities for the bifractional Brownian motion using comparison theorems for Gaussian processes.

This note takes forward a comment made in Dunford and Schwartz (LInear operators, Part 1 and describes dual of $L_1$ for general measure spaces., Comment: 4 pages

Most of the characterizations of probability distributions are based on properties of functions of possibly independent random variables. We investigate characterizations of probability distributions through properties of minima or maxima of max-independent, min-independent and quasi-independent random variables generalizing the results from independent random variables of Kotlarski (1978), Prakasa Rao (1992) and Klebanov (1973).

Multiple exciton generation (MEG) is a widely studied phenomenon in semiconductor nanocrystals and quantum dots, aimed at improving the energy conversion efficiency of solar cells. MEG is the process wherein incident photon energy is significantly larger than the band gap, and the resulting photoexcited carriers relax by generating additional electron-hole pairs, rather than decaying by heat dissipation. Here, we present an experimental demonstration of MEG in a prototype strongly correlated material, VO2, through photocurrent spectroscopy and ultrafast transient reflectivity measurements, both of which are considered the most prominent ways for detecting MEG in working devices. The key result of this paper is the observation of MEG at room temperature (in a correlated insulating phase of VO2), and the estimated threshold for MEG is 3Eg. We demonstrate an escalated photocurrent due to MEG in VO2, and quantum efficiency is found to exceed 100%. Our studies suggest that this phenomenon is a manifestation of expeditious impact ionization due to stronger electron correlations and could be exploited in a large number of strongly correlated materials., Comment: 6 pages, 5 figures, Physical Review B