On estimating the memory for finitarily markovian processes
On estimation in random fields generated by linear stochastic partial differential equations
On estimation of intrinsic volume densities of stationary random closed sets via parallel sets in the plane
A method of estimation of intrinsic volume densities for stationary random closed sets in based on estimating volumes of tiny collars has been introduced in T. Mrkvička and J. Rataj, On estimation of intrinsic volume densities of stationary random closed sets, Stoch. Proc. Appl. 118 (2008), 2, 213-231. In this note, a stronger asymptotic consistency is proved in dimension 2. The implementation of the method is discussed in detail. An important step is the determination of dilation radii in the...
On European option pricing under partial information
We consider a European option pricing problem under a partial information market, i.e., only the security's price can be observed, the rate of return and the noise source in the market cannot be observed. To make the problem tractable, we focus on gap option which is a generalized form of the classical European option. By using the stochastic analysis and filtering technique, we derive a Black-Scholes formula for gap option pricing with dividends under partial information. Finally, we apply filtering...
On evaluation of some two-dimensional normal probabilities
On exceptional systems of random integers.
On exchangeable random variables and the statistics of large graphs and hypergraphs.
On existence and an asymptotic behavior of random solutions of a class of stochastic functional-integral equations
On Existence of Local Martingale Measures for Insiders who Can Stop at Honest Times
We consider a market with two types of agents with different levels of information. In addition to a regular agent, there is an insider whose additional knowledge consists of being able to stop at an honest time Λ. We show, using the multiplicative decomposition of the Azéma supermartingale, that if the martingale part of the price process has the predictable representation property and Λ satisfies some mild assumptions, then there is no equivalent local martingale measure for the insider. This...
On existence, uniqueness and stability of solutions of multidimensional SDE's with reflecting boundary conditions
On exit laws for semigroups in weak duality
Let be a measurable semigroup and a -finite positive measure on a Lusin space . An -exit law for is a family of nonnegative measurable functions on which are finite -a.e. and satisfy for each
On exit laws for subordinated semigroups by means of -subordinators
We study the integral representation of potentials by exit laws in the framework of sub-Markovian semigroups of bounded operators acting on . We mainly investigate subordinated semigroups in the Bochner sense by means of -subordinators. By considering the one-sided stable subordinators, we deduce an integral representation for the original semigroup.
On Expectation of the Maximum for Sums of Independent Random Variables.
On extensions of Rényi conditional probability spaces
On extrapolation blowups in the scale.
On extrapolation in multiple ARMA processes
On Extrapolation of Moving Average and Autoregressive Processes
On extremal dependence of block vectors
Due to globalization and relaxed market regulation, we have assisted to an increasing of extremal dependence in international markets. As a consequence, several measures of tail dependence have been stated in literature in recent years, based on multivariate extreme-value theory. In this paper we present a tail dependence function and an extremal coefficient of dependence between two random vectors that extend existing ones. We shall see that in weakening the usual required dependence allows to...
On extremal measures for conservative particle systems
On extremal solutions of martingale problems