On randomized stopping times.
In this note we give a proof of the fact that the extremal elements of the set of randomized stopping times are exactly the stopping times.
On real zeros of random polynomials with hyperbolic elements.
On reduction of two-parameter prediction problems
We present a general method for the extension of results about linear prediction for q-variate weakly stationary processes on a separable locally compact abelian group (whose dual is a Polish space) with known values of the processes on a separable subset to results for weakly stationary processes on with observed values on . In particular, the method is applied to obtain new proofs of some well-known results of Ze Pei Jiang.
On Regression Models with Non-Square Integrable Martingale-Like Errors
On revelation transforms that characterize probability distributions.
On risk reserve under distribution constraints
The purpose of this work is a study of the following insurance reserve model: , t ∈ [0,T], P(η ≥ c) ≥ 1-ϵ, ϵ ≥ 0. Under viability-type assumptions on a pair (p,σ) the estimation γ with the property: is considered.
On Schur-convexity of expectation of weighted sum of random variables with applications.
On self-similarity and stationary problem for fragmentation and coagulation models
On semi-martingales associated with crossings
On sequences of σ-algebras
On sequential plans for the exponential class of processes
On Skorohod embedding in -dimensional brownian motion by means of natural stopping times
On small deviations of Gaussian processes using majorizing measures
We give two examples of periodic Gaussian processes, having entropy numbers of exactly the same order but radically different small deviations. Our construction is based on Knopp's classical result yielding existence of continuous nowhere differentiable functions, and more precisely on Loud's functions. We also obtain a general lower bound for small deviations using the majorizing measure method. We show by examples that our bound is sharp. We also apply it to Gaussian independent sequences and...
On smoothing properties of transition semigroups associated to a class of SDEs with jumps
We prove smoothing properties of nonlocal transition semigroups associated to a class of stochastic differential equations (SDE) in driven by additive pure-jump Lévy noise. In particular, we assume that the Lévy process driving the SDE is the sum of a subordinated Wiener process (i.e. , where is an increasing pure-jump Lévy process starting at zero and independent of the Wiener process ) and of an arbitrary Lévy process independent of , that the drift coefficient is continuous (but not...
On solutions set of a multivalued stochastic differential equation
We analyse multivalued stochastic differential equations driven by semimartingales. Such equations are understood as the corresponding multivalued stochastic integral equations. Under suitable conditions, it is shown that the considered multivalued stochastic differential equation admits at least one solution. Then we prove that the set of all solutions is closed and bounded.
On some conjecture concerning Gaussian measures of dilatations of convex symmetric sets
The paper deals with the following conjecture: if μ is a centered Gaussian measure on a Banach space F,λ > 1, K ⊂ F is a convex, symmetric, closed set, P ⊂ F is a symmetric strip, i.e. P = {x ∈ F : |x'(x)| ≤ 1} for some x' ∈ F', such that μ(K) = μ(P) then μ(λK) ≥ μ(λP). We prove that the conjecture is true under the additional assumption that K is "sufficiently symmetric" with respect to μ, in particular it is true when K is a ball in Hilbert space. As an application we give estimates of Gaussian...
On some definition of expectation of random element in metric space
We are dealing with definition of expectation of random elements taking values in metric space given by I. Molchanov and P. Teran in 2006. The approach presented by the authors is quite general and has some interesting properties. We present two kinds of new results:• conditions under which the metric space is isometric with some real Banach space;• conditions which ensure "random identification" property for random elements and almost sure convergence of asymptotic martingales.
On Some Equivalence Transformations Of Hilbert Space Valued Standard Wiener Process
On some general distributions in terms of generalized functions
On some generalized reinforced random walk on integers.