Related papers: Malliavin calculus of Bismut type without probabil…
Let $(P_t)$ be the transition semigroup of the Markov family $(X^x(t))$ defined by SDE $$ d X= b(X) dt + d Z, \qquad X(0)=x, $$ where $Z=\left(Z_1, \ldots, Z_d\right)^*$ is a system of independent real-valued L\'evy processes. Using the…
In the present paper we prove Liouville-type theorems: non-existence theorems for some complete Riemannian almost product manifolds and special mappings of complete Riemannian manifolds which generalize similar results for compact…
In this article we revisit a new notion of positivity in real semisimple Lie groups that at the same time generalizes total positivity in split real Lie groups as well as positive Lie semigroups in Hermitian Lie groups of tube type. We…
Pairwise non-isomorphic semigroups obtained from the finite inverse symmetric semigroup $\mathcal{IS}_n ,$ finite symmetric semigroup $\mathcal{T}_n$ and bicyclic semigroup by the deformed multiplication proposed by Ljapin are classified.
We establish a general Liouville type theorem for conformally invariant fully nonlinear equations.
We construct a finitely generated group $G$ without the Liouville property such that the return probability of a random walk satisfies $p_{2n}(e,e) \gtrsim e^{-n^{1/2 + o(1)}}$. Recent results suggest that $1/2$ is indeed the smallest…
In this paper we study probabilistic aspects such as (cyclic) subgroup commutativity degree and (cyclic) factorization number of ZM-groups. We show that these quantities can be computed using the sizes of the conjugacy classes of these…
Many invariants of finitely generated positive cancelative commutative semigroups can be studied from their Poincar\'e series. We offer and present several closed formulas for them. Moreover, those formulas have elementary proofs and are…
We show how to use the Malliavin calculus to obtain density estimates of the law of general centered random variables. In particular, under a non-degeneracy condition, we prove and use a new formula for the density of a random variable…
We study the relationship between the loop problem of a semigroup, and that of a Rees matrix construction (with or without zero) over the semigroup. This allows us to characterize exactly those completely zero-simple semigroups for which…
In this paper, we provide an explicit probability distribution for classification purposes. It is derived from the Bayesian nonparametric mixture of Dirichlet process model, but with suitable modifications which remove unsuitable aspects of…
Bayesian and other likelihood-based methods require specification of a statistical model and may not be fully satisfactory for inference on quantities, such as quantiles, that are not naturally defined as model parameters. In this paper, we…
In this paper we introduce a Hilbert space-valued Malliavin calculus for Poisson random measures. It is solely based on elementary principles from the theory of point processes and basic moment estimates, and thus allows for a simple…
We introduce a class of non-Moufang loops satisfying the Moufang's theorem.
This article surveys computational methods for posterior inference with intractable likelihoods, that is where the likelihood function is unavailable in closed form, or where evaluation of the likelihood is infeasible. We review recent…
A direct method for calculation of Miura type transformations via LA pair is used for the Boussinesq equation. Quadratic Miura type transformations connected with local weakly-nonlocal (Maltsev-Novikov) Hamiltonian structures. Modified…
The Stein's method is a popular method used to derive upper-bounds of distances between probability distributions. It can be viewed, in certain of its formulations, as an avatar of the semi-group or of the smart-path method used commonly in…
This paper presents a decision-theoretic approach to statistical inference that satisfies the likelihood principle (LP) without using prior information. Unlike the Bayesian approach, which also satisfies LP, we do not assume knowledge of…
On any denumerable product of probability spaces, we extend the discrete Malliavin structure for conditionally independent random variables. As a consequence, we obtain the chaos decomposition for functionals of conditionally independent…
We establish the optimal order of Malliavin-type remainders in the asymptotic density approximation formula for Beurling generalized integers. Given $\alpha\in (0,1]$ and $c>0$ (with $c\leq 1$ if $\alpha=1$), a generalized number system is…