1,720,963 research outputs found
Optimal Control of the FitzHugh?Nagumo Stochastic Model with Nonlinear Diffusion
Full text linkWe consider the existence and first order conditions of optimality for a stochastic optimal control problem inspired by the celebrated FitzHugh-Nagumo model, with nonlinear diffusion term, perturbed by a linear multiplicative Brownian-type noise. The main novelty of the present paper relies on the application of the rescaling method which allows us to reduce the original problem to a random optimal one
A Shape Theorem for a One-Dimensional Growing Particle System with a Bounded Number of Occupants per Site
Full text linkWe consider a one-dimensional discrete-space birth process with a bounded number of particle per site. Under the assumptions of the finite range of interaction, translation invariance, and non-degeneracy, we prove a shape theorem. We also derive a limit estimate and an exponential estimate on the fluctuations of the position of the rightmost particle
Calibrating FBSDEs Driven Models in Finance via NNs
No full textThe curse of dimensionality problem refers to a set of troubles arising when dealing with huge amount of data as happens, e.g., applying standard numerical methods to solve partial differential equations related to financial modeling. To overcome the latter issue, we propose a Deep Learning approach to efficiently approximate nonlinear functions characterizing financial models in a high dimension. In particular, we consider solving the Black–Scholes–Barenblatt non-linear stochastic differential equation via a forward-backward neural network, also calibrating the related stochastic volatility model when dealing with European options. The obtained results exhibit accurate approximations of the implied volatility surface. Specifically, our method seems to significantly reduce the neural network’s training time and the approximation error on the test set
Author Correction: Heat transfer analysis of fractional model of couple stress Casson tri-hybrid nanofluid using dissimilar shape nanoparticles in blood with biomedical applications
No full textAuthor correction w.r.t. Acknowledgements sectio
Asymptotic Expansion for a Black–Scholes Model with Small Noise Stochastic Jump-Diffusion Interest Rate
No full textIn the present paper we study the asymptotic expansion for a Black–Scholes model with small noise stochastic jump-diffusion interest rate. In particular, we consider the case when the small perturbation is due to a general, but small, noise of Lévy type. Moreover, we provide explicit expressions for the involved expansion coefficients as well as accurate estimates on the remainders
Stochastic port--Hamiltonian systems
Full text linkIn the present work we formally extend the theory of port-Hamiltonian systems
to include random perturbations. In particular, suitably choosing the space of
flow and effort variables we will show how several elements coming from
possibly different physical domains can be interconnected in order to describe
a dynamic system perturbed by general continuous semimartingale. Relevant
enough, the noise does not enter into the system solely as an external random
perturbation, since each port is itself intrinsically stochastic. Coherently to
the classical deterministic setting, we will show how such an approach extends
existing literature of stochastic Hamiltonian systems on pseudo-Poisson and
pre-symplectic manifolds. Moreover, we will prove that a power-preserving
interconnection of stochastic port-Hamiltonian systems is a stochastic
port-Hamiltonian system as well
Asymptotic shape and the speed of propagation of continuous-time continuous-space birth processes
Full text linkWe formulate and prove a shape theorem for a continuous-time continuous-space stochastic growth model under certain general conditions. Similar to the classical lattice growth models, the proof makes use of the subadditive ergodic theorem. A precise expression for the speed of propagation is given in the case of a truncated free-branching birth rate
Invariant measures for sdes driven by lévy noise: A case study for dissipative nonlinear drift in infinite dimension
Full text linkWe study a class of nonlinear stochastic partial differential equations with dissipative nonlinear drift, driven by Levy noise. We define a Hilbert-Banach setting in which we prove existence and uniqueness of solutions under general assumptions on the drift and the Levy noise. We then prove a decomposition of the solution process into a stationary component, the law of which is identified with the unique invariant probability measure mu of the process, and a component which vanishes asymptotically for large times in the L-P (mu)-sense, for all 1 <= p < + infinity
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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