31 citations · 137 across the 73 of their papers we have counts for
13 papers · 1 filter
Stochastic control problems and HJB equations with excluded parameters of random inputs
Nikolai Dokuchaev
This paper introduces a new type of second order stochastic backward Hamilton-Jacobi-Bellman (HJB) equations for optimal stochastic control problems with a currently observable but…
Optimal energy storing and selling in continuous time stochastic multi-battery setting
Nikolai Dokuchaev
The paper suggests a new stochastic model for energy producing, dispatching, and storing in the multi-battery setting that takes into account the topology of the system of the link…
Sub-ideal causal smoothing filters for real sequences
Nikolai Dokuchaev
The paper considers causal smoothing of the real sequences, i.e.,discrete time processes in a deterministic setting. A family of causal linear time-invariant filters is suggested.…
Causal band-limitness and predictability criterions for one-sided sequences
Nikolai Dokuchaev
The paper studies frequency characteristics and predictability of real sequences, i.e., discrete time processes in deterministic setting. We consider band-limitness and predictabil…
Optimal replication of random vectors by ordinary integrals
Nikolai Dokuchaev
We consider a problem of replication of random vectors by ordinary integrals in the setting when a underlying random variable is generated by a Wiener process. The goal is to find…
On causal extrapolation of sequences with applications to forecasting
Nikolai Dokuchaev
The paper suggests a method of extrapolation of notion of one-sided semi-infinite sequences representing traces of two-sided band-limited sequences; this features ensure uniqueness…
Predictors for discrete time processes with energy decay on higher frequencies
Nikolai Dokuchaev
The predictability of discrete-time processes is studied in a deterministic setting. A family of one-step-ahead predictors is suggested for processes of which the energy decays at…
On causal band-limited mean square approximation
Nikolai Dokuchaev
We study causal dynamic approximation of non-bandlimited processes by band-limited processes such that a part of the historical path of the underlying process is approximated in $L…
Frequency Theorem for discrete time stochastic system with multiplicative noise
Peter Situmbeko Nalitolela, Nikolai Dokuchaev
In this paper we consider the problem of minimizing a quadratic functional for a discrete-time linear stochastic system with multiplicative noise, on a standard probability space,…
A frequency criterion for the existence of an optimal control for Ito equations
Nikolai Dokuchaev
The following optimization problem is considered. For a linear vector Ito equation. it is required to find an optimal deterministic control vector which minimizes a quadratic the f…
On sub-ideal causal smoothing filters
Nikolai Dokuchaev
Smoothing causal linear time-invariant filters are studied for continuous time processes. The paper suggests a family of causal filters with almost exponential damping of the energ…
The integral estimations for ordinary differential equations and its application to the non-smooth optimal control problems
Nikolai Dokuchaev
The paper studies integral functionals with non-smooth functions from L_2 defined on solutions of ODEs. Some regularity is obtained in the form of estimates of L_2-norm for these f…
Predictability of band-limited, high-frequency, and mixed processes in the presence of ideal low-pass filters
Nikolai Dokuchaev
Pathwise predictability of continuous time processes is studied in deterministic setting. We discuss uniform prediction in some weak sense with respect to certain classes of inputs…