Shorter Notes: A Note on Levy's Brownian Process on the Hilbert Sphere

1972 ◽  
Vol 33 (1) ◽  
pp. 207
Author(s):  
Peggy Tang Strait
Keyword(s):  
Brownian Process ◽  
Hilbert Sphere

scholarly journals A note on Lévy’s Brownian process on the Hilbert sphere

1972 ◽  
Vol 33 (1) ◽  
pp. 207-207
Author(s):  
Peggy Tang Strait
Keyword(s):  
Brownian Process ◽  
Hilbert Sphere

scholarly journals Optimal Exploitation of a General Renewable Natural Resource under State and Delay Constraints

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2053
Author(s):  
M’hamed Gaïgi ◽  
Idris Kharroubi ◽  
Thomas Lim
Keyword(s):  
Differential Equation ◽  
Natural Resource ◽  
Market Price ◽  
Programming Approach ◽  
Infinite Time ◽  
Delay Constraints ◽  
Dynamic Programming Approach ◽  
Brownian Process ◽  
Renewable Natural Resource ◽  
The Value Function

In this work, we study an optimization problem arising in the management of a natural resource over an infinite time horizon. The resource is assumed to evolve according to a logistic stochastic differential equation. The manager is allowed to harvest the resource and sell it at a stochastic market price modeled by a geometric Brownian process. We assume that there are delay constraints imposed on the decisions of the manager. More precisely, starting harvesting order and selling order are executed after a delay. By using the dynamic programming approach, we characterize the value function as the unique solution to an original partial differential equation. We complete our study with some numerical illustrations.

Characterization of fractal Brownian process in laser damaged photodiodes

1994 ◽  
Author(s):  
Woei-Yun Ho ◽  
Chun C. Ma ◽  
Robert W. Bene ◽  
A. B. Buckman ◽  
Rodger M. Walser ◽  
...  
Keyword(s):  
Brownian Process

scholarly journals Inference of population genetic structure from temporal samples of DNA

2019 ◽  
Author(s):  
Olivier François ◽  
Séverine Liégeois ◽  
Benjamin Demaille ◽  
Flora Jay
Keyword(s):  
Allele Frequency ◽  
Random Mating ◽  
Principal Component ◽  
Estimation Algorithm ◽  
Frequency Drift ◽  
Fast Estimation ◽  
Data Representations ◽  
Brownian Process ◽  
Multiple Strains ◽  
Individual Scores

AbstractThe recent years have seen a growing number of studies investigating evolutionary questions using ancient DNA techniques and temporal samples of DNA. To address these questions, one of the most frequently-used algorithm is based on principal component analysis (PCA). When PCA is applied to temporal samples, the sample dates are, however, ignored during analysis, which could lead to some misinterpretations of the results. Here we introduce a new factor analysis (FA) method for which individual scores are corrected for the effect of allele frequency drift through time. Based on a diffusion approximation, our approach approximates allele frequency drift in a random mating population by a Brownian process. Exact solutions for estimates of corrected factors are obtained, and a fast estimation algorithm is presented. We compared data representations obtained from the FA method with PCA and with PC projections in simulations of divergence and admixture scenarios. Then we applied FA with correction for temporal drift to study the evolution of hepatitis C virus in a patient infected by multiple strains, and to describe the population structure of ancient European samples.

Decision-Making Coordination within Three-Echelon Supply Chains

2011 ◽  
pp. 93-107
Author(s):  
Jairo R. Montoya-Torres
Keyword(s):  
Decision Making ◽  
Supply Chain ◽  
Process Simulation ◽  
Simulation Models ◽  
Chain Model ◽  
Total System ◽  
Direct Relation ◽  
Supply Chain Model ◽  
Brownian Process ◽  
The Impact

Supply chain performance is highly influenced by the coordination level between its members, which needs information sharing. In this paper we consider a three-echelon direct sell supply chain model and focus on the problem of coordinated decision-making between its members. Our contribution is a first approach that measures the impact of the degree of coordination between the members. Demand behavior is modeled using a geometric Brownian process. Simulation models are run in order to analyze various cooperation scenarios. Our results show a direct relation between the degree of coordination within the supply chain and the total system cost. Although this result is intuitive, our simulations allowed us to quantify such a relation and in which measure these costs are whether or not associated to imperfect coordination.

THE COMPLEXITY OF BROWNIAN PROCESSES RUN WITH NONLINEAR CLOCKS

2011 ◽  
Vol 25 (01) ◽  
pp. 1-10 ◽  
Author(s):  
MOONGYU PARK ◽  
JOHN H. CUSHMAN
Keyword(s):  
Brownian Motion ◽  
Fractal Dimension ◽  
Anomalous Diffusion ◽  
Mean Square Displacement ◽  
Scaling Exponent ◽  
Near Surface ◽  
Surface Ocean ◽  
Power Law Exponent ◽  
Brownian Process ◽  
Turbulent Fluids

Anomalous diffusion occurs in many branches of physics. Examples include diffusion in confined nanofilms, Richardson turbulence in the atmosphere, near-surface ocean currents, fracture flow in porous formations and vortex arrays in rotating flows. Classically, anomalous diffusion is characterized by a power law exponent related to the mean-square displacement of a particle or squared separation of pairs of particles: 〈|X(t)|2〉 ~tγ. The exponent γ is often thought to relate to the fractal dimension of the underlying process. If γ > 1 the flow is super-diffusive, if it equals 1 it is classical, otherwise it is sub-diffusive. In this work we illustrate how time-changed Brownian position processes can be employed to model sub-, super-, and classical diffusion, while time-changed Brownian velocity processes can be used to model super-diffusion alone. Specific examples presented include transport in turbulent fluids and renormalized transport in porous media. Intuitively, a time-changed Brownian process is a classical Brownian motion running with a nonlinear clock (Bm-nlc). The major difference between classical and Bm-nlc is that the time-changed case has nonstationary increments. An important novelty of this approach is that, unlike fractional Brownian motion, the fractal dimension of the process (space filling character) driving anomalous diffusion as modeled by Bm-nlc positions or velocities does not change with the scaling exponent, γ.

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