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

Ergodic theory | Random environments | Periodic functions | Random walks

Journal Article

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

Ellipticity | Random walk in random environments | Ballisticity

Journal Article

2015, Graduate studies in mathematics, ISBN 9780821875780, Volume 162, xiv, 318

Book

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

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

Journal Article

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

Optimal harvesting | Stochastic perturbations | Predator–prey | Time delay | Predator-prey | SYSTEM | MATHEMATICS, APPLIED | DIFFUSION | NOISE | FLUCTUATING POPULATIONS | EXTINCTION | RANDOM-ENVIRONMENTS

Journal Article

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

Gompertz model | Stochastic differential equations | Fisheries management | Profit optimization | Random environments | FISHERIES | Fisheries | Fish industry | Models | Comparative analysis | Fishing | Differential equations

Journal Article

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

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

Journal Article

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

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

Journal Article

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

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

Journal Article

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

Markov chains | Percolation | Random environments | Random walk | Random conductances | RANDOM-WALK | TAIL | STATISTICS & PROBABILITY

Journal Article

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

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

Journal Article

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

SYSTEM | Stochastic noises | MATHEMATICS, APPLIED | Stability | DYNAMICS | Beddington-DeAngelis functional response | Time delay | EXTINCTION | RANDOM-ENVIRONMENTS

Journal Article

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

Research Article | INSTRUMENTS & INSTRUMENTATION | DYNAMICS | RISK | FLUCTUATING POPULATIONS | EXTINCTION | AUTOMATION & CONTROL SYSTEMS | RANDOM-ENVIRONMENTS | ENGINEERING, ELECTRICAL & ELECTRONIC

Journal Article

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

Optimal harvesting | Stochastic perturbations | Ergodic method | SYSTEM | MATHEMATICS, APPLIED | POLICY | MECHANICS | EQUATIONS | PHYSICS, MATHEMATICAL | FLUCTUATING POPULATIONS | RANDOM-ENVIRONMENTS | JUMPS | Harvesting | Analysis | Models

Journal Article

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

PARTICLE | PHYSICS, FLUIDS & PLASMAS | RANDOM-WALK | DYNAMICS | EXPONENT | DIFFUSION | PHYSICS, MATHEMATICAL | DIMENSIONAL RANDOM-ENVIRONMENTS

Journal Article

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

TRANSPORT | MODEL | PHYSICS, MATHEMATICAL | PHYSICS, FLUIDS & PLASMAS | RANDOM-ENVIRONMENTS

Journal Article

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

DIFFUSION | LAW | PHYSICS, MULTIDISCIPLINARY | RANDOM-WALKS | DIMENSIONAL RANDOM-ENVIRONMENTS | Physics - Statistical Mechanics

Journal Article

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

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

Journal Article

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

exact enumeration | self-avoiding walks | percolation clusters | THRESHOLD | SERIES | PHYSICS, MULTIDISCIPLINARY | DISORDERED MEDIA | DILUTED LATTICES | CRITICAL-BEHAVIOR | BACKBONE | PHYSICS, MATHEMATICAL | RANDOM-ENVIRONMENTS

Journal Article

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

Ellipticity | Random walk in random environments | TRANSIENT RANDOM-WALKS | Ballisticity | STATISTICS & PROBABILITY | DIRICHLET ENVIRONMENT

Journal Article

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