A maximal inequality of non-negative submartingale.
A maximum likelihood estimator of an inhomogeneous Poisson point processes intensity using beta splines
The problem of estimating the intensity of a non-stationary Poisson point process arises in many applications. Besides non parametric solutions, e. g. kernel estimators, parametric methods based on maximum likelihood estimation are of interest. In the present paper we have developed an approach in which the parametric function is represented by two-dimensional beta-splines.
A *-mixing convergence theorem for convex set valued processes.
A model and application of binary random sequence with probabilities depending on history
This paper presents a model of binary random sequence with probabilities depending on previous sequence values as well as on a set of covariates. Both these dependencies are expressed via the logistic regression model, such a choice enables an easy and reliable model parameters estimation. Further, a model with time-depending parameters is considered and method of solution proposed. The main objective is then the application dealing with both artificial and real data cases, illustrating the method...
A model of atomic radiation
A multiplier theorem for Fourier series in several variables
We define a new type of multiplier operators on , where is the N-dimensional torus, and use tangent sequences from probability theory to prove that the operator norms of these multipliers are independent of the dimension N. Our construction is motivated by the conjugate function operator on , to which the theorem applies as a particular example.
A necessary and sufficient condition for the -coalescent to come down from the infinity.
A new approach to the analysis of a discrete round-robin queue
We identify the regions of parameters of the arriving stream in which the ergodic, critical, or supercritical properties of the branching chain are established.
A New Class of Unbalanced Haar Wavelets That Form an Unconditional Basis for L... on General Measure Spaces.
A new intrinsic construction of the gaussian measure in ; with application
A new kind of augmentation of filtrations
Let (Ω, , ()t≥0, ) be a filtered probability space satisfying the usual assumptions: it is usually not possible to extend to (theσ-algebra generated by ()t≥0) a coherent family of probability measures () indexed byt≥0, each of them being defined on . It is known that for instance, on the Wiener space, this extension problem has a positive answer if one takes the filtration generated by the coordinate process, made right-continuous, but can have a negative answer if one takes its usual augmentation....
A new kind of augmentation of filtrations
Let (Ω, , ()t≥0, ) be a filtered probability space satisfying the usual assumptions: it is usually not possible to extend to (the σ-algebra generated by ()t≥0) a coherent family of probability measures () indexed by t≥0, each of them being defined on . It is known that for instance, on the Wiener space, this extension problem has a positive answer if one takes the filtration generated by the coordinate process, made right-continuous, but can have a negative answer if one takes its usual...
A new proof of Kellerer’s theorem
In this paper, we present a new proof of the celebrated theorem of Kellerer, stating that every integrable process, which increases in the convex order, has the same one-dimensional marginals as a martingale. Our proof proceeds by approximations, and calls upon martingales constructed as solutions of stochastic differential equations. It relies on a uniqueness result, due to Pierre, for a Fokker-Planck equation.
A new proof of Kellerer’s theorem
In this paper, we present a new proof of the celebrated theorem of Kellerer, stating that every integrable process, which increases in the convex order, has the same one-dimensional marginals as a martingale. Our proof proceeds by approximations, and calls upon martingales constructed as solutions of stochastic differential equations. It relies on a uniqueness result, due to Pierre, for a Fokker-Planck equation.
A Non-Central Functional Limit Theorem for Quadratic Forms in Martingale Difference Sequences
A nonergodic version of Gordin's CLT for integrable stationary processes
A non-linear Riesz respresentation in probabilistic potential theory
A non-Markovian process with unbounded -variation.
A non-nonstandard proof of Reimers' existence result for heat SPDEs.
A non-reversible semi-martingale