Small noise asymptotics for a stochastic growth model by Noah Williams

Cover of: Small noise asymptotics for a stochastic growth model | Noah Williams

Published by National Bureau of Economic Research in Cambridge, MA .

Written in English

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Subjects:

  • Stochastic processes.,
  • Economic development -- Mathematical models.

Edition Notes

Book details

StatementNoah Williams.
SeriesNBER working paper series ;, working paper 10194, Working paper series (National Bureau of Economic Research : Online) ;, working paper no. 10194.
ContributionsNational Bureau of Economic Research.
Classifications
LC ClassificationsHB1
The Physical Object
FormatElectronic resource
ID Numbers
Open LibraryOL3476824M
LC Control Number2005616368

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Small Noise Asymptotics for a Stochastic Growth Model Article in Journal of Economic Theory (2) December with 24 Reads How we measure 'reads'. Get this from a library. Small noise asymptotics for a stochastic growth model.

[Noah Williams; National Bureau of Economic Research.]. Small Noise Asymptotics for a Stochastic Growth Model Noah Williams. NBER Working Paper No. Issued in December NBER Program(s):Economic Fluctuations and Growth We develop analytic asymptotic methods to characterize time series properties of nonlinear dynamic stochastic models.

Small noise asymptotics for a stochastic growth model. Author links open overlay panel Noah Williams a b. Show more. We focus on a stochastic growth model which is representative of the models underlying much of modern macroeconomics. Taking limits as the stochastic shocks become small, we derive a functional central limit theorem, a large Cited by: Get this from a library.

Small noise asymptotics for a stochastic growth model. [Noah Williams; National Bureau of Economic Research.] -- "We develop analytic asymptotic methods to characterize time series properties of nonlinear dynamic stochastic models.

We focus on a stochastic growth model which is representative of the models. Noah Williams, "Small Noise Asymptotics for a Stochastic Growth Model," NBER Working PapersNational Bureau of Economic Research, Inc.

Noah Williams, "Small Noise Asymptotics for a Stochastic Growth Model," Computing in Economics and FinanceSociety for Computational Economics. Request PDF | Small Time Asymptotics for SPDEs with Locally Monotone Coefficients | This work aims to prove the small time large deviation principle (LDP) for a class of stochastic partial.

4 Non-stochastic growth model In the non-stochastic growth model, the problem of the representative agent is to allocate resources between consumption and investment in capital, as in the continuous Small noise asymptotics for a stochastic growth model book Ramsey model.

Capital is completely malleable, being able to be transformed into consumption at a rate of one-to-one. Since the model is File Size: KB. Dynamical system models with delayed dynamics and small noise arise in a variety of applications in science and engineering.

In many applications, stable equilibrium or periodic behavior is critical to a well functioning system. Sufficient conditions for the stability of equilibrium points or periodic orbits of certain deterministic dynamical systems with delayed dynamics are known and it is Cited by: 2.

Fields –, ) for the small noise asymptotics problem are adapted to solve the small time asymptotics problem. The results obtained in this way improve on some results of Zhang (Ann. Probab. 28(2)–, ).Cited by: 2. Small-time asymptotics for an uncorrelated local-stochastic volatility model Martin Forde⁄ Antoine Jacquiery 20th April Abstract We add some rigour to the work of Henry-Labordµere[20], Lewis[25] and Paulot[28] on the small-time behaviour of a local-stochastic volatility model with zero correlation at leading order.

6 runs of stochastic logistic growth model, carrying capacity = Demographic stochasticity has its biggest impact on small populations 6 runs of stochastic logistic growth model, carrying capacity = A stochastic version of the geometric population growth model N tt 1 λ()tN •Suppose that has the following probability distribution.

The Brock-Mirman Model V Proposition In the stochastic optimal growth problem described above, the policy function for next period™s capital stock, π(k,z), is strictly increasing in both of its arguments. Proof: I By assumption u is di⁄erentiable and from the Proposition above V is di⁄erentiable in k.

Solving the Stochastic Growth Model by Using Quadrature Methods and Value-Function Iterations George Tauchen Department of Economics, Duke University, Durham, NC This article presents a solution algorithm for the capital growth model.

The algorithm uses value- function iterations on a discrete state space. We compute a sharp small-time estimate for implied volatility under a general uncorrelated local-stochastic volatility model.

For this we use the Bellaiche \\cite{Bel81} heat kernel expansion combined with Laplace's method to integrate over the volatility variable on a compact set, and (after a gauge transformation) we use the Davies \\cite{Dav88} upper bound Cited by: The corresponding Itô stochastic equation describes a process on a Hilbert space with dissipative nonlinear, non globally Lipschitz drift and a Gaussian noise.

Under smoothness assumptions on the nonlinearity, asymptotics to all orders in a small parameter in front of the noise are given, with uniform estimates on the remainders. Bernstein-von Mises theorem and small noise asymptotics of Bayes estimators for parabolic stochastic partial differential equations, Theory of Stochastic Processes 23 (1) (), Sequential maximum likelihood estimation in nonlinear non-Markov diffusion type processes, Dynamic Systems and Applications.

27 (1) (), The logistic growth model 13 The competition model 15 2. Stochastic analysis 18 The stochastic logistic growth model 18 The stochastic competition model 21 Alternative models 22 3.

Comparison of deterministic and stochastic analysis of Gause’s data 24 III. Asymptotics for rough stochastic volatility models Martin Forde∗ Hongzhong Zhang† November 2, Abstract Using the large deviation principle (LDP) for a re-scaled fractional Brownian motion BH t where the rate function is de ned via the reproducing kernel Hilbert space, we compute small-time asymptotics forFile Size: KB.

Small noise asymptotics. A variational representation for infinite dimensional BM. Applications to large deviations. Systems driven by fractional Brownian motions. Poisson random measures. Moderate deviations. : Stochastic Resonance: A Mathematical Approach in the Small Noise Limit (Mathematical Surveys and Monographs) (): Samuel Herrmann, Peter Imkeller, Ilya Pavlyukevich, Dierk Peithmann: BooksCited by: For the stochastic wave equation in spatial dimension 1 with space–time white noise, Conus et al.

show that if the initial position and velocity are bounded and measurable functions, then the moment Lyapunov exponents satisfy m ¯ p ≤ C p 3 / 2 for p ≥ 2, and m ¯ 2 ≥ c (κ / 2) 1 / 2 for positive initial data. The difference in the Cited by: 8. Small Noise Asymptotics for a Stochastic Growth Model w Published: Williams, Noah.

"Small Noise Asymptotics For A Stochastic Growth Model," Journal of Economic Theory,v(2,Dec), citation courtesy of. March Modeling Model Uncertainty with Alexei Onatski: w Published: Alexei Onatski & Noah Williams, nonlinear term has at most polynomial growth and is such that the whole system is dissipative.

The corresponding It^o stochastic equation describes a process on a Hilbert space with dissipative nonlinear drift and a Gaussian noise. Under smoothness assumptions on the non-linearity, asymptotics to all orders in a small pa. Williams, N.,Small noise asymptotics for a stochastic growth model, Journal of Economic Theory, (2), – zbMATH MathSciNet CrossRef Google Scholar [] Yaari, M.E.,A law of large numbers in the theory of consumer’s choice under uncertainty, Journal of Economic The – zbMATH MathSciNet CrossRef Google ScholarCited by: The Brock-Mirman Model Optimal Growth under Uncertainty The Brock-Mirman Model V PropositionIn the stochastic optimal growth problem described above, the policy function for next period™s capital stock, p(k,z), is strictly increasing in both of its arguments.

Proof: By assumption u is di⁄erentiable and from the Proposition above V is. c Novem ,Christopher D. Carroll BrockMirman The Brock-Mirman Stochastic Growth Model Brock and Mirman() provided the first optimizing growth modelFile Size: KB.

This book is intended as a beginning text in stochastic processes for stu-dents familiar with elementary probability calculus. Its aim is to bridge the gap between basic probability know-how and an intermediate-level course in stochastic processes-for example, A First Course in Stochastic Processes, by the present authors.

This paper investigates the asymptotic behavior of the random-time ruin probability in a time-dependent renewal risk model with pairwise quasi-asymptotically independent and subexponential claims, where the time-dependence structure is constructed between a claim size and its inter-arrival time, and described by a conditional tail probability of the claim size given the inter Cited by: 1.

agent, optimal, stochastic growth model. Decision rules as well as simulated time series are compared. The differences among the methods turned out to be quite substantial for certain aspects of the growth model. Therefore, researchers might want to be careful not to rely blindly on the results of any chosen numerical solution method in applied File Size: KB.

Though these two types of noise arise from different causes, their adverse effect on learning is similar. The overfitting occurs because the model attempts to fit the (stochastic or deterministic) noise (that part of the data that it cannot model) at the expense of fitting that part of the data which it.

Stochastic modeling is a form of financial model that is used to help make investment decisions. This type of modeling forecasts the probability of various outcomes under different conditions Author: Will Kenton.

Stochastic Resonance A Mathematical Approach in the Small Noise Limit Samuel Herrmann Peter Imkeller Ilya Pavlyukevich Dierk Peithmann. fusion) model and the associated reduced (finite state Markov chain) model one gets essentially different tuning scenarios.

We therefore propose—in arbitrary fi. of economic growth (see [6], [7], [17] and [20]) and in asymptotic methods (see [13] and [14]). Lipster et al’s paper deals with a stochastic control system in conti-nuous time with a finite horizon and with nonnegative costs.

In [16] the stochastic problem is approximated by a deterministic system when the noise intensitiy "is small. A SIMPLE CALIBRATION PROCEDURE OF STOCHASTIC VOLATILITY MODELS WITH JUMPS BY SHORT TERM ASYMPTOTICS Alexey MEDVEDEV and Olivier SCAILLET a1 a HEC Genève and FAME, Université de Genève, Bd Carl Vogt, CH - Genève 4, Suisse.

[email protected], [email protected] by: rate function is defined via the reproducing kernel Hilbert space, we compute small-time asymptotics for a correlated fractional stochastic volatility model of the form dSt = S tσ(Yt)(¯ρdWt + ρdBt), dYt = dB H where σ is α-H¨older continuous for some α ∈ (0,1]; in particular, we show that tH−12 logS t satisfies the.

DSO Benefits.─The MGS stochastic model is one tool currently used by DSO to determine hydrologic risk. This study will allow the Probabilistic Flood Hazard Cadre to identify the strengths, weaknesses, and limitations of the MGS model and other stochastic models that will enable DSO managers to effectively and correctly apply the information.

7 – 2 ness Cycles, published in Dennis Robertson and A.C. Pigou were among the leading economists who developed theories to try to explain Mitchell’s empirical ob-servations on business cycles in the pre-depression period.

This page is concerned with the stochastic modelling as applied to the insurance industry. For other stochastic modelling applications, please see Monte Carlo method and Stochastic asset mathematical definition, please see Stochastic process.

"Stochastic" means being or having a random variable.A stochastic model is a tool for estimating probability distributions of.

model are constant, however. This is called the steady state. Assume that the production function takes the following form: Y t= A tK 1 t (Z tN t) 0. Stochastic Resonance: A Mathematical Approach in the Small Noise Limit Samuel Herrmann, Peter Imkeller, Ilya Pavlyukevich, Dierk Peithmann Stochastic resonance is a phenomenon arising in a wide spectrum of areas in the sciences ranging from physics through neuroscience to chemistry and biology.mators under infill asymptotics and increasing domain asymptotics, in each case assuming that the process is observed over an equally-spaced grid.

In Stein (), he further studied the infill asymptotics for modified likelihood estima-tors assuming a general periodic Gaussian process in model (). Ying (the asymptotic mutual information per dimension in this model lim n!1I(X;Y), cf.

Theorem below. The resulting asymptotic value is proved to coincide with the asymptotic value in the stochastic block model, as established in Theorem In other words, the per-dimension mutual information turns out to be universal across multiple noise models.

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