Conditionally monotone independence
نویسنده
چکیده
We define the notion of conditionally monotone product as a part of conditionally free product, which naturally includes monotone and Boolean products. Then we define conditionally monotone cumulants which are useful to calculate the limit distributions in central limit theorem and Poisson’s law of small numbers. Moreover, we introduce deformed convolutions arising from the conditionally monotone convolution of probability measures and compute the limit distributions. In order to understand the validity of cumulants, we discuss what are cumulants of a given convolution product in general.
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