arXiv subjects

R. Liptser

Publications and source records attributed to R. Liptser.

22 records · Page 2Linked to original sources

arXiv2003

MDP for integral functionals of fast and slow processes with averaging

We establish large deviation principle (LDP) for the family of vector-valued random processes $(X^ε,Y^ε),ε\to 0$ defined as $$ X^ε_t=\frac{1}{ε^κ}\int_0^t H(ξ^ε_s,Y^ε_s)ds, dY^ε_t=F(ξ^ε_t,Y^ε_t)dt+ Dε^{1/2-κ}G(ξ^ε_t,Y^ε_t)dW_t,$$ where $W_t$ is Wiener process and $ξ^ε_t$ is fast ergodic diffusion. We show that, under $κ<{1/2}$ or less and Veretennikov-Khasminskii type condition for fast diffusion, the LDP holds with rate function of Freidlin-Wentzell's type.

math.PR↗

arXiv2002

On-line tracking of a smooth regression function

We construct an on-line estimator with equidistant design for tracking a smooth function from Stone-Ibragimov-Khasminskii class. This estimator has the optimal convergence rate of risk to zero in sample size. The procedure for setting coefficients of the estimator is controlled by a single parameter and has a simple numerical solution. The off-line version of this estimator allows to eliminate a boundary layer. Simulation results are given.

math.ST↗

arXiv2002

On diffusion approximation with discontinuous coefficients

Convergence of stochastic processes with jumps to diffusion processes is investigated in the case when the limit process has discontinuous coefficients. An example is given in which the diffusion approximation of a queueing model yields a diffusion process with discontinuous diffusion and drift coefficients.

math.PR↗

arXiv2002

On exponential stability of Wonham filter

We give elementary proof of a stability result concerning an exponential asymptotic ($t\to\infty$) for filtering estimates generated by wrongly initialized Wonham filter. This proof is based on new exponential bound having independent interest.

math.PR↗