What random variable generates a bounded potential?
What was Nicolo Tartaglia doing in the night to Ash Wednesday of the year 1523 in Verona. (Was machte Nicolo Tartaglia in der Nacht zum Aschermittwoch des Jahres 1523 in Verona.)
When does a randomly weighted self-normalized sum converge in distribution?
When is a Riesz distribution a complex measure?
Let be the Riesz distribution on a simple Euclidean Jordan algebra, parametrized by . I give an elementary proof of the necessary and sufficient condition for to be a locally finite complex measure (= complex Radon measure).
Where did the Brownian particle go?
Where does randomness lead in spacetime?
We provide an alternative algebraic and geometric approach to the results of [I. Bailleul, Probab. Theory Related Fields141 (2008) 283–329] describing the asymptotic behaviour of the relativistic diffusion.
Where the typical set partitions meet and join.
Which moments of a logarithmic derivative imply quasiinvariance.
Which values of the volume growth and escape time exponent are possible for a graph?
Why Jordan algebras are natural in statistics: quadratic regression implies Wishart distributions
If the space of quadratic forms in is splitted in a direct sum and if and are independent random variables of , assume that there exist a real number such that and real distinct numbers such that for any in We prove that this happens only when , when can be structured in a Euclidean Jordan algebra and when and have Wishart distributions corresponding to this structure.
Why the Kemeny Time is a constant
We present a new fundamental intuition forwhy the Kemeny feature of a Markov chain is a constant. This new perspective has interesting further implications.
Why -additive (fuzzy) measures?
The paper is concerned with generalized (i. e. monotone and possibly non-additive) measures. A discussion concerning the classification of these measures, according to the type and amount of non-additivity, is done. It is proved that -additive measures appear naturally as solutions of functional equations generated by the idea of (possible) non additivity.
Wick product and stochastic partial differential equations with Poisson measure
Wiener functionals of second order and their Lévy measures.
Wiener integral for the coordinate process under the σ-finite measure unifying Brownian penalisations
Wiener integral for the coordinate process is defined under the σ-finite measure unifying Brownian penalisations, which has been introduced by [Najnudel et al., C. R. Math. Acad. Sci. Paris345 (2007) 459–466] and [Najnudel et al., MSJ Memoirs19. Mathematical Society of Japan, Tokyo (2009)]. Its decomposition before and after last exit time from 0 is studied. This study prepares for the author's recent study [K. Yano, J. Funct. Anal.258 (2010) 3492–3516] of Cameron-Martin formula for the...
Wiener integral for the coordinate process under the σ-finite measure unifying brownian penalisations
Wiener integral for the coordinate process is defined under the σ-finite measure unifying Brownian penalisations, which has been introduced by [Najnudel et al., C. R. Math. Acad. Sci. Paris 345 (2007) 459–466] and [Najnudel et al., MSJ Memoirs 19. Mathematical Society of Japan, Tokyo (2009)]. Its decomposition before and after last exit time from 0 is studied. This study prepares for the author's recent study [K. Yano, J. Funct. Anal. 258 (2010) 3492–3516] of Cameron-Martin formula for the σ-finite...
Wiener integral in the space of sequences of real numbers
Wiener measures on certain Banach spaces over non-archimedean local fields
Wiener process with reflection in non-smooth narrow tubes.
Wiener soccer and its generalization.