Birth and death on a Brownian flow: a Feller semigroup and its generator and a martingale problem

1996 ◽  
Vol 33 (1) ◽  
pp. 71-87 ◽  
Author(s):  
Michael J. Phelan
Keyword(s):  
Markov Process ◽  
Spatial Configuration ◽  
Martingale Problem ◽  
Stochastic Flow ◽  
Transition Semigroup ◽  
Feller Semigroup ◽  
System Of Particles ◽  
Particle Process

We consider a system of particles in birth and death on a stochastic flow. The system includes a particle process tracking the spatial configuration of live particles on the flow. The particle process is a Markov process on the space of bounded counting measures. We show that its transition semigroup is a Feller semigroup and exhibit its pregenerator. The pregenerator defines a martingale problem. We show that the particle process solves the problem uniquely.

Birth and death on a Brownian flow: a Feller semigroup and its generator and a martingale problem

1996 ◽  
Vol 33 (01) ◽  
pp. 71-87 ◽  
Author(s):  
Michael J. Phelan
Keyword(s):  
Markov Process ◽  
Spatial Configuration ◽  
Martingale Problem ◽  
Stochastic Flow ◽  
Transition Semigroup ◽  
Feller Semigroup ◽  
System Of Particles ◽  
Particle Process

We consider a system of particles in birth and death on a stochastic flow. The system includes a particle process tracking the spatial configuration of live particles on the flow. The particle process is a Markov process on the space of bounded counting measures. We show that its transition semigroup is a Feller semigroup and exhibit its pregenerator. The pregenerator defines a martingale problem. We show that the particle process solves the problem uniquely.

A Girsanov transformation for birth and death on a Brownian flow

1996 ◽  
Vol 33 (1) ◽  
pp. 88-100 ◽  
Author(s):  
Michael J. Phelan
Keyword(s):  
Spatial Configuration ◽  
Particle System ◽  
Continuous Change ◽  
Drift Diffusion ◽  
Absolutely Continuous ◽  
Death Rates ◽  
Girsanov Transformation ◽  
Girsanov Formula ◽  
System Of Particles ◽  
Particle Process

We consider a system of particles in birth and death on a Brownian flow. The system includes a particle process tracking the spatial configuration of live particles on the flow. The particle process is a Markov process on the space of counting measures. The system depends on a handful of parameters including a rate of drift, diffusion, birth, and killing. We exhibit a Girsanov formula for the absolutely continuous change of particle system by way of a change of drift, birth, and killing rates. We can only allow for a restrictive change of drift on the flow, but for fairly unrestrictive change of birth and death rates. The result is therefore of some interest in problems of statistical inference from passive transport of transient tracers.

A Girsanov transformation for birth and death on a Brownian flow

1996 ◽  
Vol 33 (01) ◽  
pp. 88-100
Author(s):  
Michael J. Phelan
Keyword(s):  
Spatial Configuration ◽  
Particle System ◽  
Continuous Change ◽  
Drift Diffusion ◽  
Absolutely Continuous ◽  
Death Rates ◽  
Girsanov Transformation ◽  
Girsanov Formula ◽  
System Of Particles ◽  
Particle Process

We consider a system of particles in birth and death on a Brownian flow. The system includes a particle process tracking the spatial configuration of live particles on the flow. The particle process is a Markov process on the space of counting measures. The system depends on a handful of parameters including a rate of drift, diffusion, birth, and killing. We exhibit a Girsanov formula for the absolutely continuous change of particle system by way of a change of drift, birth, and killing rates. We can only allow for a restrictive change of drift on the flow, but for fairly unrestrictive change of birth and death rates. The result is therefore of some interest in problems of statistical inference from passive transport of transient tracers.

Asymptotic Analysis of Nonlinear Stochastic Equations With Rapidly Oscillating and Decaying Components

2003 ◽  
Author(s):  
N. Sri Namachchivaya ◽  
H. J. Van Roessel
Keyword(s):  
Dynamical System ◽  
Markov Process ◽  
Martingale Problem ◽  
Nonlinear Dynamical System ◽  
Stochastic Equations ◽  
Limiting Behavior ◽  
Nonlinear Dynamical ◽  
Nonlinear Stochastic Equations ◽  
Lower Dimensional ◽  
Quadratic And Cubic Nonlinearities

We consider a noisy n-dimensional nonlinear dynamical system containing rapidly oscillating and decaying components. We extend the results of Papanicolaou and Kohler and Namachchivaya and Lin; these results state that as the noise becomes smaller, a lower dimensional Markov process characterizes the limiting behavior. Our approach springs from a direct consideration of the martingale problem and considers both quadratic and cubic nonlinearities.

scholarly journals Juggler's Exclusion Process

2012 ◽  
Vol 49 (01) ◽  
pp. 266-279
Author(s):  
Lasse Leskelä ◽  
Harri Varpanen
Keyword(s):  
Markov Process ◽  
Gibbs Measure ◽  
Equilibrium Distribution ◽  
Exclusion Process ◽  
Jump Height ◽  
The Family ◽  
System Of Particles ◽  
Unit Speed ◽  
Positive Integers ◽  
Special Case

Juggler's exclusion process describes a system of particles on the positive integers where particles drift down to zero at unit speed. After a particle hits zero, it jumps into a randomly chosen unoccupied site. We model the system as a set-valued Markov process and show that the process is ergodic if the family of jump height distributions is uniformly integrable. In a special case where the particles jump according to a set-avoiding memoryless distribution, the process reaches its equilibrium in finite nonrandom time, and the equilibrium distribution can be represented as a Gibbs measure conforming to a linear gravitational potential.

ON THE UNIQUENESS OF THE MARTINGALE PROBLEM

1996 ◽  
Vol 07 (06) ◽  
pp. 775-810 ◽  
Author(s):  
ODIMBOLEKO OKITALOSHIMA ◽  
JAN A. VAN CASTEREN
Keyword(s):  
Martingale Problem ◽  
Continuous Functions ◽  
Linear Operators ◽  
Bounded Linear ◽  
Feller Semigroup ◽  
The Maximum Principle ◽  
Dissipative Operators ◽  
Vector Sum ◽  
Locally Compact Hausdorff Space ◽  
Well Posed

Let E be a second countable locally compact Hausdorff space and let L be a linear operator with domain D(L) and range R(L) in C0(E). Suppose that D(L) is dense in E and that the operator L possesses the Korovkin property or, more generally, the Stone property with respect to some large collection of continuous functions (cf. Definition 3.8). For every x∈E the martingale problem is well-posed if and only if there exists a unique extension of L that generates a Feller semigroup in C0(E). Next let L0 be the generator of a Feller semigroup in C0(E) and let L1 and T be linear operators with the following properties: the operator I–T has range D(L1), the domain of L1, L1 verifies the maximum principle, the vector sum of the spaces R(I–T) and R(L1(I–T)) is dense in C0(E), and [Formula: see text]. Then there exists at most one linear extension L of the operator L1 for which LT is bounded and that generates a Feller semigroup. Similarly, if the martingale problem is solvable for L1, then it is uniquely solvable for L1, provided that the operator [Formula: see text] is a bounded linear map in C0(E). Here (ℙx, X(t)) is a solution to the martingale problem for L1. Some related results for dissipative operators in a Banach space are presented as well.

The multitype measure branching process

1990 ◽  
Vol 22 (1) ◽  
pp. 49-67 ◽  
Author(s):  
Luis G. Gorostiza ◽  
Jose A. Lopez-Mimbela
Keyword(s):  
Small Particle ◽  
Branching Process ◽  
Martingale Problem ◽  
Single Type ◽  
System Of Particles

The existence of the multitype measure branching process is established as a small particle limit of a system of particles of several types in Rd with immigration undergoing migration, branching and mutation. The process is characterized as a solution of a martingale problem. The single-type case was studied by Dawson (1975), (1977) and Watanabe (1968).

scholarly journals Juggler's Exclusion Process

2012 ◽  
Vol 49 (1) ◽  
pp. 266-279 ◽  
Author(s):  
Lasse Leskelä ◽  
Harri Varpanen
Keyword(s):  
Markov Process ◽  
Gibbs Measure ◽  
Equilibrium Distribution ◽  
Exclusion Process ◽  
Jump Height ◽  
The Family ◽  
System Of Particles ◽  
Unit Speed ◽  
Positive Integers ◽  
Special Case

Juggler's exclusion process describes a system of particles on the positive integers where particles drift down to zero at unit speed. After a particle hits zero, it jumps into a randomly chosen unoccupied site. We model the system as a set-valued Markov process and show that the process is ergodic if the family of jump height distributions is uniformly integrable. In a special case where the particles jump according to a set-avoiding memoryless distribution, the process reaches its equilibrium in finite nonrandom time, and the equilibrium distribution can be represented as a Gibbs measure conforming to a linear gravitational potential.

The multitype measure branching process

1990 ◽  
Vol 22 (01) ◽  
pp. 49-67 ◽  
Author(s):  
Luis G. Gorostiza ◽  
Jose A. Lopez-Mimbela
Keyword(s):  
Small Particle ◽  
Branching Process ◽  
Martingale Problem ◽  
Single Type ◽  
System Of Particles

The existence of the multitype measure branching process is established as a small particle limit of a system of particles of several types inRdwith immigration undergoing migration, branching and mutation. The process is characterized as a solution of a martingale problem. The single-type case was studied by Dawson (1975), (1977) and Watanabe (1968).

The Effect of Nonlinear Amplitude Growth on the Speech Perception Benefits Provided by a Single-Sided Vocoder

2019 ◽  
Vol 62 (3) ◽  
pp. 745-757 ◽  
Author(s):  
Jessica M. Wess ◽  
Joshua G. W. Bernstein
Keyword(s):  
Transfer Functions ◽  
Spatial Configuration ◽  
Free Field ◽  
Spatial Separation ◽  
Compression And Expansion ◽  
Interaural Difference ◽  
Interaural Differences ◽  
Single Sided Deafness ◽  
Perceptual Separation ◽  
Loudness Growth

PurposeFor listeners with single-sided deafness, a cochlear implant (CI) can improve speech understanding by giving the listener access to the ear with the better target-to-masker ratio (TMR; head shadow) or by providing interaural difference cues to facilitate the perceptual separation of concurrent talkers (squelch). CI simulations presented to listeners with normal hearing examined how these benefits could be affected by interaural differences in loudness growth in a speech-on-speech masking task.MethodExperiment 1 examined a target–masker spatial configuration where the vocoded ear had a poorer TMR than the nonvocoded ear. Experiment 2 examined the reverse configuration. Generic head-related transfer functions simulated free-field listening. Compression or expansion was applied independently to each vocoder channel (power-law exponents: 0.25, 0.5, 1, 1.5, or 2).ResultsCompression reduced the benefit provided by the vocoder ear in both experiments. There was some evidence that expansion increased squelch in Experiment 1 but reduced the benefit in Experiment 2 where the vocoder ear provided a combination of head-shadow and squelch benefits.ConclusionsThe effects of compression and expansion are interpreted in terms of envelope distortion and changes in the vocoded-ear TMR (for head shadow) or changes in perceived target–masker spatial separation (for squelch). The compression parameter is a candidate for clinical optimization to improve single-sided deafness CI outcomes.

Sign in / Sign up

Export Citation Format

Share Document