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Poisson's equation plays a fundamental role as a tool for performance evaluation and optimization of Markov chains. For continuous-time birth-death chains with possibly unbounded transition and cost rates as addressed herein, when…
In this paper we consider cases of existence of invariant measure, additional first integrals, and Poisson structure in a problem of rigid body's rolling without sliding on plane and sphere. The problem of rigid body's motion on plane was…
A spring-block model governed by threshold dynamics and driven by temporally increasing spring constants is investigated. Due to its novel multiplicative driving, criticality occurs even with periodic boundary conditions via a mechanism…
A well-specified parametrization for single-input/single-output (SISO) linear port-Hamiltonian systems amenable to structure-preserving supervised learning is provided. The construction is based on controllable and observable normal form…
We consider a dynamical elasto-plasticity system with Kelvin--Voigt viscosity and linear kinematic hardening of Melan--Prager type. The model is formulated in a variational framework in which a constraint set for the stress evolves in time…
In this paper, we relax the power parameter of instantaneous variance and develop a new stochastic volatility plus jumps model that generalize the Heston model and 3/2 model as special cases. This model has two distinctive features. First,…
We study the tamed magnetohydrodynamics equations, introduced recently in a paper by the author, perturbed by multiplicative Wiener noise of transport type on the whole space $\mathbb{R}^{3}$ and on the torus $\mathbb{T}^{3}$. In a first…
An analog of the Meir-Wingreen formula for the steady-state heat current through a model molecular junction is derived. The expression relates the heat current to correlation functions that involve operators only acting on the degrees of…
We construct a class of iterated stochastic integrals with respect to Brownian motion on an abstract Wiener space which allows for the definition of Brownian motions on a general class of infinite-dimensional nilpotent Lie groups based on…
We construct exact time-dependent solutions of the supergravity equations of motion in which two initially non-singular branes, one with positive and the other with negative tension, move together and annihilate each other in an…
We parameterize the phase space density by time dependent diffeomorphic, Poisson preserving transformations on phase space acting on a reference density solution. We can look at these as transformations which fix time on the extended space…
We propose a constructive approach to building temporal point processes that incorporate dependence on their history. The dependence is modeled through the conditional density of the duration, i.e., the interval between successive event…
We establish a microstructural foundation of the rough Bergomi model. Specifically, we consider a sequence of order driven financial market models where orders to buy or sell an asset arrive according to a Poisson process and have a long…
While the original Ait-Sahalia interest rate model has been found considerable use as a model for describing time series evolution of interest rates, it may not possess adequate specifications to explain responses of interest rates to…
This paper presents a framework for binary autoregressive time series in which each observation is a Bernoulli variable whose success probability evolves with past outcomes and probabilities, in the spirit of GARCH-type dynamics,…
Some phase space transport properties for a conservative bouncer model are studied. The dynamics of the model is described by using a two-dimensional measure preserving mapping for the variables velocity and time. The system is…
Reservoir computing systems are constructed using a driven dynamical system in which external inputs can alter the evolving states of a system. These paradigms are used in information processing, machine learning, and computation. A…
Using the Euler--Maruyama technique, we show that a class of Wiener processes exist that are obtained by computing an arbitrary positive power of them. This can be accomplished with a proper set of definitions that makes meaningful the…
We establish finite-dimensional central limit theorems for local, additive, interaction functions of temporally evolving point processes. The dynamics are those of a spatial Poisson process on the flat torus with points subject to a…
We consider parameter estimation of stochastic differential equations driven by a Wiener process and a compound Poisson process as small noises. The goal is to give a threshold-type quasi-likelihood estimator and show its consistency and…