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1. Full Text Detecting periodicity from the trajectory of a random walk in random environment
by Rémillard, Bruno N and Vaillancourt, Jean
Statistics and Probability Letters, ISSN 0167-7152, 12/2019, Volume 155, p. 108568
For nearest neighbor univariate random walks in a periodic environment, where the probability of moving depends on a periodic function, we show how to estimate... 
Ergodic theory | Random environments | Periodic functions | Random walks
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2. Full Text Local trapping for elliptic random walks in random environments in Z d
by Fribergh, Alexander and Kious, Daniel
Probability Theory and Related Fields, ISSN 0178-8051, 08/2016, Volume 165, Issue 3-4, pp. 795 - 834
To access, purchase, authenticate, or subscribe to the full-text of this article, please visit this link: http://dx.doi.org/10.1007/s00440-015-0646-4 We... 
Ellipticity | Random walk in random environments | Ballisticity
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3. A course on large deviations with an introduction to Gibbs measures
by Rassoul-Agha, Firas and Seppäläinen, Timo O
2015, Graduate studies in mathematics, ISBN 9780821875780, Volume 162, xiv, 318
Measure theory | Probabilities | Large deviations
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4. Full Text Random walks with barriers
by Novikov, Dmitry S and Fieremans, Els and Jensen, Jens H and Helpern, Joseph A
Nature Physics, ISSN 1745-2473, 06/2011, Volume 7, Issue 6, pp. 508 - 514
Restrictions to molecular motion by barriers (membranes) are ubiquitous in porous media, composite materials and biological tissues. A major challenge is to... 
TIME-DEPENDENT DIFFUSION | CELL-MEMBRANE | NMR | COEFFICIENT | PHYSICS, MULTIDISCIPLINARY | DISORDERED MEDIA | SYSTEMS | POROUS-MEDIA | MODEL | STATIC DISORDER | RANDOM-ENVIRONMENTS | Molecular biology | Time dependence | Membranes | Monte Carlo methods | Computer simulation | Barriers | Disorders | Constrictions | Transport
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5. Full Text Optimal harvesting policy of a stochastic predator–prey model with time delay
by Liu, Meng
Applied Mathematics Letters, ISSN 0893-9659, 10/2015, Volume 48, pp. 102 - 108
This paper concerns the optimal harvesting of a stochastic delay predator–prey model. Sufficient and necessary conditions for the existence of an optimal... 
Optimal harvesting | Stochastic perturbations | Predator–prey | Time delay | Predator-prey | SYSTEM | MATHEMATICS, APPLIED | DIFFUSION | NOISE | FLUCTUATING POPULATIONS | EXTINCTION | RANDOM-ENVIRONMENTS
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6. Full Text Fisheries management in randomly varying environments: Comparison of constant, variable and penalized efforts policies for the Gompertz model
by Brites, Nuno M and Braumann, Carlos A
Fisheries Research, ISSN 0165-7836, 08/2019, Volume 216, pp. 196 - 203
In a previous paper, we discussed the use of an optimal variable effort fishing policy versus an optimal sustainable constant effort fishing policy in terms of... 
Gompertz model | Stochastic differential equations | Fisheries management | Profit optimization | Random environments | FISHERIES | Fisheries | Fish industry | Models | Comparative analysis | Fishing | Differential equations
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7. Full Text Analysis of a stochastic tri-trophic food-chain model with harvesting
by Liu, Meng and Bai, Chuanzhi
Journal of Mathematical Biology, ISSN 0303-6812, 9/2016, Volume 73, Issue 3, pp. 597 - 625
We consider a tri-trophic stochastic food-chain model with harvesting. We first establish critical values between persistence in mean and extinction for each... 
60H10 | 60H30 | 92D25 | Mathematical and Computational Biology | Stochastic control | Mathematics | Applications of Mathematics | Management of natural resources | Optimization under uncertainties | SYSTEM | FLUCTUATING ENVIRONMENTS | PERSISTENCE | EQUATIONS | RANDOM PERTURBATION | PREDATOR | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | DYNAMICS | LOGISTIC POPULATION | EXTINCTION | RANDOM-ENVIRONMENTS | Food Chain | Environment | Stochastic Processes | Models, Biological | Learning models (Stochastic processes) | Usage | Food chains (Ecology) | Models
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8. Full Text Competitive Lotka–Volterra population dynamics with jumps
by Bao, Jianhai and Mao, Xuerong and Yin, Geroge and Yuan, Chenggui
Nonlinear Analysis, ISSN 0362-546X, 2011, Volume 74, Issue 17, pp. 6601 - 6616
This paper considers competitive Lotka–Volterra population dynamics with jumps. The contributions of this paper are as follows. (a) We show that a stochastic... 
Variation-of-constants formula | Jumps | Extinction | Stochastic boundedness | Lotka–Volterra model | Lyapunov exponent | MATHEMATICS, APPLIED | PERSISTENCE | STABILITY | EQUATIONS | Lotka-Volterra model | MATHEMATICS | MODELS | SYSTEMS | RANDOM-ENVIRONMENTS | Parathyroid hormone | Statistics | Analysis | Nonlinear dynamics | Dynamic tests | Predator-prey simulation | Lyapunov exponents | Differential equations | Mathematical models | Lotka-Volterra equations
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9. Full Text Persistence and extinction in stochastic non-autonomous logistic systems
by Liu, Meng and Wang, Ke
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2011, Volume 375, Issue 2, pp. 443 - 457
This paper studies two widely used stochastic non-autonomous logistic models. For the first system, sufficient conditions for extinction, non-persistence in... 
Persistence | Extinction | Non-autonomous logistic model | Stochastic perturbation | POLLUTED ENVIRONMENT | MATHEMATICS, APPLIED | STABILITY | PREDATOR-PREY MODEL | NOISE | RANDOM PERTURBATION | MATHEMATICS | LOTKA-VOLTERRA MODEL | FLUCTUATIONS | POPULATION-DYNAMICS | DELAY | RANDOM-ENVIRONMENTS
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10. Full Text On heat kernel decay for the random conductance model
by Boukhadra, Omar
Statistics and Probability Letters, ISSN 0167-7152, 02/2018, Volume 133, pp. 23 - 27
We study discrete time random walks in an environment of i.i.d. non-negative bounded conductances in . We are interested in the anomaly of the heat kernel... 
Markov chains | Percolation | Random environments | Random walk | Random conductances | RANDOM-WALK | TAIL | STATISTICS & PROBABILITY
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11. Full Text Stochastic switching in biology: From genotype to phenotype
by Bressloff, Paul C
Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 02/2017, Volume 50, Issue 13, p. 133001
There has been a resurgence of interest in non-equilibrium stochastic processes in recent years, driven in part by the observation that the number of molecules... 
large deviations | transcriptional bursting | stochastic gene expression | quorum sensing | metastability | random environments | bacterial growth | APPROXIMATE TRAVELING-WAVES | TRANSPORT-EQUATIONS | PHYSICS, MULTIDISCIPLINARY | COLLECTIVE BEHAVIOR | PHYSICS, MATHEMATICAL | MARKOV-PROCESSES | MULTILEVEL MONTE-CARLO | ASYMPTOTIC ANALYSIS | GENE-EXPRESSION | CHEMICAL-REACTION NETWORKS | WEAK-NOISE LIMIT | MULTIPLE EQUILIBRIA
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12. Full Text Global asymptotic stability of a stochastic delayed predator-prey model with Beddington-DeAngelis functional response
by Liu, M and Bai, CZ
APPLIED MATHEMATICS AND COMPUTATION, ISSN 0096-3003, 01/2014, Volume 226, pp. 581 - 588
This paper is concerned with a stochastic predator-prey system with Beddington-DeAngelis functional response and time delay. Sufficient conditions for global... 
SYSTEM | Stochastic noises | MATHEMATICS, APPLIED | Stability | DYNAMICS | Beddington-DeAngelis functional response | Time delay | EXTINCTION | RANDOM-ENVIRONMENTS
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13. Full Text Optimal harvesting strategies for stochastic ecosystems
by Tran, Ky Quan and Yin, George
IET Control Theory & Applications, ISSN 1751-8644, 10/2017, Volume 11, Issue 15, pp. 2521 - 2530
Focusing on multidimensional stochastic Lotka–Volterra type ecosystems in which multiple species are interacting, this study aims developing optimal harvesting... 
Research Article | INSTRUMENTS & INSTRUMENTATION | DYNAMICS | RISK | FLUCTUATING POPULATIONS | EXTINCTION | AUTOMATION & CONTROL SYSTEMS | RANDOM-ENVIRONMENTS | ENGINEERING, ELECTRICAL & ELECTRONIC
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14. Full Text Optimal Harvesting of a Stochastic Logistic Model with Time Delay
by Liu, Meng and Bai, Chuanzhi
Journal of Nonlinear Science, ISSN 0938-8974, 2015, Volume 25, Issue 2, pp. 277 - 289
This note is concerned with the optimal harvesting of a stochastic logistic model with time delay. The classical optimal harvesting question of this type of... 
Optimal harvesting | Stochastic perturbations | Ergodic method | SYSTEM | MATHEMATICS, APPLIED | POLICY | MECHANICS | EQUATIONS | PHYSICS, MATHEMATICAL | FLUCTUATING POPULATIONS | RANDOM-ENVIRONMENTS | JUMPS | Harvesting | Analysis | Models
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15. Full Text Persistence of Brownian motion in a shear flow
by Takikawa, Yoshinori and Orihara, Hiroshi
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 12/2013, Volume 88, Issue 6
The persistence of a Brownian particle in a shear flow is investigated. The persistence probability P(t), which is the probability that the particle does not... 
PARTICLE | PHYSICS, FLUIDS & PLASMAS | RANDOM-WALK | DYNAMICS | EXPONENT | DIFFUSION | PHYSICS, MATHEMATICAL | DIMENSIONAL RANDOM-ENVIRONMENTS
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16. Full Text Spatially inhomogeneous transition probabilities as memory effects for diffusion in statistically homogeneous random velocity fields
by Suciu, Nicolae
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 05/2010, Volume 81, Issue 5, p. 056301
Whenever one uses translation invariant mean Green's functions to describe the behavior in the mean and to estimate dispersion coefficients for diffusion in... 
TRANSPORT | MODEL | PHYSICS, MATHEMATICAL | PHYSICS, FLUIDS & PLASMAS | RANDOM-ENVIRONMENTS
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17. Full Text Fluctuations of time averages for Langevin dynamics in a binding force field
by Dechant, A and Lutz, E and Kessler, D.A and Barkai, E
Physical Review Letters, ISSN 0031-9007, 12/2011, Volume 107, Issue 24, p. 240603
We derive a simple formula for the fluctuations of the time average (x) over bar (t) around the thermal mean < x >(eq) for overdamped Brownian motion in a... 
DIFFUSION | LAW | PHYSICS, MULTIDISCIPLINARY | RANDOM-WALKS | DIMENSIONAL RANDOM-ENVIRONMENTS | Physics - Statistical Mechanics
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18. Optimal harvesting of a stochastic delay competitive model
by Liu, Meng and Bai, Chuanzhi
Discrete and Continuous Dynamical Systems - Series B, ISSN 1531-3492, 06/2017, Volume 22, Issue 4, pp. 1493 - 1508
In this paper an n-Species stochastic delay competitive model with harvesting is proposed. Some dynamical properties of the model are considered. We first... 
Optimal harvesting | Stochastic perturbations | Time delay | Competitive model | MATHEMATICS, APPLIED | stochastic perturbations | STABILITY | EQUATIONS | time delay | RANDOM PERTURBATION | PREDATOR-PREY SYSTEM | competitive model | DYNAMICS | LOGISTIC POPULATION | FLUCTUATING POPULATIONS | RANDOM-ENVIRONMENTS | JUMPS
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19. Full Text Exact enumeration of self-avoiding walks on critical percolation clusters in 2-7 dimensions
by Fricke, Niklas and Janke, Wolfhard
Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 06/2017, Volume 50, Issue 26, p. 264002
We study self-avoiding walks on critical percolation clusters by means of a recently developed exact enumeration method, which can handle walks of several... 
exact enumeration | self-avoiding walks | percolation clusters | THRESHOLD | SERIES | PHYSICS, MULTIDISCIPLINARY | DISORDERED MEDIA | DILUTED LATTICES | CRITICAL-BEHAVIOR | BACKBONE | PHYSICS, MATHEMATICAL | RANDOM-ENVIRONMENTS
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20. Full Text Local trapping for elliptic random walks in random environments in Z(d)
by Fribergh, A and Kious, D
PROBABILITY THEORY AND RELATED FIELDS, ISSN 0178-8051, 08/2016, Volume 165, Issue 3-4, pp. 795 - 834
We consider elliptic random walks in i.i.d. random environments on . The main goal of this paper is to study under which ellipticity conditions local trapping... 
Ellipticity | Random walk in random environments | TRANSIENT RANDOM-WALKS | Ballisticity | STATISTICS & PROBABILITY | DIRICHLET ENVIRONMENT
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