On a Schröder equation arising in branching processes.
On a stochastic inventory model with deteriorating items.
On a stopped brownian motion formula of H. M. Taylor
On a theorem of Cartan
On a triplet of exponential brownian functionals
On absorption times and Dirichlet eigenvalues
This paper gives a stochastic representation in spectral terms for the absorption time T of a finite Markov chain which is irreducible and reversible outside the absorbing point. This yields quantitative informations on the parameters of a similar representation due to O'Cinneide for general chains admitting real eigenvalues. In the discrete time setting, if the underlying Dirichlet eigenvalues (namely the eigenvalues of the Markov transition operator restricted to the functions vanishing on...
On adaptive control for the continuous time-varying JLQG problem
In this paper the adaptive control problem for a continuous infinite time-varying stochastic control system with jumps in parameters and quadratic cost is investigated. It is assumed that the unknown coefficients of the system have limits as time tends to infinity and the boundary system is absolutely observable and stabilizable. Under these assumptions it is shown that the optimal value of the quadratic cost can be reached based only on the values of these limits, which, in turn, can be estimated...
On adaptive control of a partially observed Markov chain
A control problem for a partially observable Markov chain depending on a parameter with long run average cost is studied. Using uniform ergodicity arguments it is shown that, for values of the parameter varying in a compact set, it is possible to consider only a finite number of nearly optimal controls based on the values of actually computable approximate filters. This leads to an algorithm that guarantees nearly selfoptimizing properties without identifiability conditions. The algorithm is based...
On additive and multiplicative (controlled) Poisson equations
Assuming that a Markov process satisfies the minorization property, existence and properties of the solutions to the additive and multiplicative Poisson equations are studied using splitting techniques. The problem is then extended to the study of risk sensitive and risk neutral control problems and corresponding Bellman equations.
On an extension of jump-type symmetric Dirichlet forms.
On an identity in law obtained by A. Földes and P. Révész
On an optimum principle for partially observed controlled jump Markovian processes
On analyticity of Ornstein-Uhlenbeck semigroups
Let be a transition semigroup of the Hilbert space-valued nonsymmetric Ornstein-Uhlenbeck process and let denote its Gaussian invariant measure. We show that the semigroup is analytic in if and only if its generator is variational. In particular, we show that the transition semigroup of a finite dimensional Ornstein-Uhlenbeck process is analytic if and only if the Wiener process is nondegenerate.
On asymptotic independence of the exit moment and position from a small domain for diffusion processes
If ξ(t) is the solution of homogeneous SDE in R m, and T ∃ is the first exit moment of the process from a small domain D ∃, then the total expansion for the following functional showing independence of the exit time and exit place is
On ballistic diffusions in random environment
On Brownian and Poissonian Convolution Semigroups on the Infinite Dimensional Torus
On brownian local time
On calculating the Laplace transform of a special quadratic functional of the Ornstein-Uhlenbeck velocity process
On Cauchy-Dirichlet problem in half-space for linear integro-differential equations in weighted Hölder spaces.
On certain almost brownian filtrations